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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83750.
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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt.
Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet.
Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Mendoza, Quispe Wilfredo. "K-teoría de C*-álgebras." Master's thesis, Universidad Nacional Mayor de San Marcos, 2014. https://hdl.handle.net/20.500.12672/3780.
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El objetivo principal de esta tesis es calcular la K-Teoría de las C∗-Álgebras y con
aplicación al cálculo de la K-Teoría del Álgebra de Cuntz y Álgebra de Toeplitz
mediante la K-teoría de las C∗-Álgebras de grafos dirigidos.Tesis
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Knapper, Andrew. "Derivations on certain banach algebras." Thesis, University of Birmingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368411.
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Zabroda, Olga Nikolaievna. "Generalized convolution operators and asymptotic spectral theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200602061.
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The dissertation contributes to the further advancement of the theory of various classes of discrete and continuous (integral) convolution operators. The thesis is devoted to the study of sequences of matrices or operators which are built up in special ways from generalized discrete or continuous convolution operators. The generating functions depend on three variables and this leads to considerably more complicated approximation sequences. The aim was to obtain for each case a result analogous to the first Szegö limit theorem providing the first order asymptotic formula for the spectra of regular convolutions.
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Seidel, Markus [Verfasser], Peter [Akademischer Betreuer] Junghanns, Peter [Gutachter] Junghanns, Bernd [Akademischer Betreuer] Silbermann, and Vladimir S. [Gutachter] Rabinovich. "On some Banach Algebra Tools in Operator Theory / Markus Seidel ; Gutachter: Peter Junghanns, Vladimir S. Rabinovich ; Peter Junghanns, Bernd Silbermann." Chemnitz : Universitätsbibliothek Chemnitz, 2012. http://d-nb.info/1214243320/34.
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Zarka, Benjamin. "La propriété de décroissance rapide hybride pour les groupes discrets." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4057.
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Un groupe finiment engendré G a la propriété RD lorsque l'algèbre de Sobolev du groupe H^s(G) s'injecte dans la C^*-algèbre réduite C^*_r(G). Cette inclusion permet de contrôler la norme de l'opérateur de convolution sur l^2(G) par des normes l^2 pondérées, et induit des isomorphismes en K-théorie. Il est connu que la présence de sous-groupes moyennables à croissance sur-polynomiale est une obstruction à cette propriété. Parallèlement à cela, on dispose toujours d'une inclusion canonique de l^1(G) dans C^*_r(G), mais cette estimation est en général moins fine que celle donnée par RD, et l'existence d'isomorphismes de K-théorie découlant de cette inclusion est un problème généralement ouvert qui est souvent issu de la combinaison des conjectures de Bost et Baum-Connes. C'est pourquoi, dans cette thèse, nous présenterons une version relative de la propriété RD appelée propriété RD_H basée sur une interpolation entre les normes l^1 et l^2 paramétrée par un sous-groupe H de G. Nous verrons que cette propriété peut être vue comme une généralisation aux cas des sous-groupes non distingués du fait que le quotient G/H ait la propriété RD. Nous étudierons certaines propriétés géométriques liées à l'espace G/H permettant de déduire ou d'infirmer la propriété RD_H. En particulier, nous nous pencherons sur le cas où H est un sous-groupe co-moyennable de G et le cas où G est un groupe relativement hyperbolique par rapport au sous-groupe H. Nous montrerons que la propriété RD_H nous permet d'obtenir une famille d'isomorphismes en K-théorie paramétrée par le choix du sous-groupe H, et d'obtenir une borne inférieure concernant la probabilité de retour dans le sous-groupe H d'une marche aléatoire symétrique. Une autre partie de la thèse est consacrée à l'existence d'un isomorphisme entre les groupes de K-théorie des algèbres l^1(G) et C^*_r(G) où l'on prouve la véracité de ce résultat pour certains produits semi-directs en combinant deux types de suites exactes sans faire intervenir les conjectures de Bost et Baum-ConnesA finitely generated group G has the property RD when the Sobolev space H^s(G) embeds in the group reduced C^*-algebra C^*_r(G). This embedding induces isomorphisms in K-theory, and allows to upper-bound the operator norm of the convolution on l^2(G) by weighted l^2 norms. It is known that if G contains an amenable subgroup with superpolynomial growth, then G cannot have property RD. In another hand, we always have the canonical inclusion of l^1(G) in C^*_r(G), but this estimation is generally less optimal than the estimation given by the property RD, and in most of cases, it needs to combine Bost and Baum-Connes conjectures to know if that inclusion induces K-theory isomorphisms. That's the reason why, in this thesis, we define a relative version of property RD by using an interpolation norm between l^1 and l^2 which depends on a subgroup H of G, and we call that property: property RD_H. We will see that property RD_H can be seen as an analogue for non-normal subgroups to the fact that G/H has property RD, and we will study what kind of geometric properties on G/H can imply or deny the property RD_H. In particular, we care about the case where H is a co-amenable subgroup of G, and the case where G is relatively hyperbolic with respect to H. We will show that property RD_H induces isomorphisms in K-theory, and gives us a lower bound concerning the return probability in the subgroup H for a symmetric random walk. Another part of the thesis is devoted to show that if G is a certain kind of semi-direct product, the inclusion l^1(G)subset C^*_r(G) induces isomorphisms in K-theory, we prove this statement by using two types of exact sequences without using Bost and Baum-Connes conjectures
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Heymann, Retha. "Fredholm theory in general Banach algebras." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4265.
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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm theory in the context of bounded linear operators on Banach spaces to a theory in a Banach algebra setting. A bounded linear operator T on a Banach space X is Fredholm if it has closed range and the dimension of its kernel as well as the dimension of the quotient space X/T(X) are finite. The index of a Fredholm operator is the integer dim T−1(0)−dimX/T(X). Weyl operators are those Fredholm operators of which the index is zero. Browder operators are Fredholm operators with finite ascent and descent. Harte’s generalisation is motivated by Atkinson’s theorem, according to which a bounded linear operator on a Banach space is Fredholm if and only if its coset is invertible in the Banach algebra L(X) /K(X), where L(X) is the Banach algebra of bounded linear operators on X and K(X) the two-sided ideal of compact linear operators in L(X). By Harte’s definition, an element a of a Banach algebra A is Fredholm relative to a Banach algebra homomorphism T : A ! B if Ta is invertible in B. Furthermore, an element of the form a + b where a is invertible in A and b is in the kernel of T is called Weyl relative to T and if ab = ba as well, the element is called Browder. Harte consequently introduced spectra corresponding to the sets of Fredholm, Weyl and Browder elements, respectively. He obtained several interesting inclusion results of these sets and their spectra as well as some spectral mapping and inclusion results. We also convey a related result due to Harte which was obtained by using the exponential spectrum. We show what H. du T. Mouton and H. Raubenheimer found when they considered two homomorphisms. They also introduced Ruston and almost Ruston elements which led to an interesting result related to work by B. Aupetit. Finally, we introduce the notions of upper and lower semi-regularities – concepts due to V. M¨uller. M¨uller obtained spectral inclusion results for spectra corresponding to upper and lower semi-regularities. We could use them to recover certain spectral mapping and inclusion results obtained earlier in the thesis, and some could even be improved.
AFRIKAANSE OPSOMMING: Hierdie tesis is ‘n studie van ’n veralgemening deur R. Harte (sien [9]) van Fredholm-teorie in die konteks van begrensde lineˆere operatore op Banachruimtes tot ’n teorie in die konteks van Banach-algebras. ’n Begrensde lineˆere operator T op ’n Banach-ruimte X is Fredholm as sy waardeversameling geslote is en die dimensie van sy kern, sowel as di´e van die kwosi¨entruimte X/T(X), eindig is. Die indeks van ’n Fredholm-operator is die heelgetal dim T−1(0) − dimX/T(X). Weyl-operatore is daardie Fredholm-operatore waarvan die indeks gelyk is aan nul. Fredholm-operatore met eindige styging en daling word Browder-operatore genoem. Harte se veralgemening is gemotiveer deur Atkinson se stelling, waarvolgens ’n begrensde lineˆere operator op ’n Banach-ruimte Fredholm is as en slegs as sy neweklas inverteerbaar is in die Banach-algebra L(X) /K(X), waar L(X) die Banach-algebra van begrensde lineˆere operatore op X is en K(X) die twee-sydige ideaal van kompakte lineˆere operatore in L(X) is. Volgens Harte se definisie is ’n element a van ’n Banach-algebra A Fredholm relatief tot ’n Banach-algebrahomomorfisme T : A ! B as Ta inverteerbaar is in B. Verder word ’n Weyl-element relatief tot ’n Banach-algebrahomomorfisme T : A ! B gedefinieer as ’n element met die vorm a + b, waar a inverteerbaar in A is en b in die kern van T is. As ab = ba met a en b soos in die definisie van ’n Weyl-element, dan word die element Browder relatief tot T genoem. Harte het vervolgens spektra gedefinieer in ooreenstemming met die versamelings van Fredholm-, Weylen Browder-elemente, onderskeidelik. Hy het heelparty interessante resultate met betrekking tot insluitings van die verskillende versamelings en hulle spektra verkry, asook ’n paar spektrale-afbeeldingsresultate en spektraleinsluitingsresultate. Ons dra ook ’n verwante resultaat te danke aan Harte oor, wat verkry is deur van die eksponensi¨ele-spektrum gebruik te maak. Ons wys wat H. du T. Mouton en H. Raubenheimer verkry het deur twee homomorfismes gelyktydig te beskou. Hulle het ook Ruston- en byna Rustonelemente gedefinieer, wat tot ’n interessante resultaat, verwant aan werk van B. Aupetit, gelei het. Ten slotte stel ons nog twee begrippe bekend, naamlik ’n onder-semi-regulariteit en ’n bo-semi-regulariteit – konsepte te danke aan V. M¨uller. M¨uller het spektrale-insluitingsresultate verkry vir spektra wat ooreenstem met bo- en onder-semi-regulariteite. Ons kon dit gebruik om sekere spektrale-afbeeldingsresultate en spektrale-insluitingsresultate wat vroe¨er in hierdie tesis verkry is, te herwin, en sommige kon selfs verbeter word.
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Muzundu, Kelvin. "Spectral theory in commutatively ordered banach algebras." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71619.
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Albuquerque, Philipe Thadeo Lima Ferreira [UNESP]. "Ponto fixo: uma introdução no ensino médio." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/110607.
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000790735.pdf: 1590232 bytes, checksum: 5297d173df2a824606d944767eb1610c (MD5)O principal objetivo deste trabalho consiste na produção de um referencial teórico relacionado aos conceitos de ponto fixo, que possibilite, aos alunos do Ensino Médio, o desenvolvimento de habilidades e competências relacionadas à Matemática. Neste trabalho são colocadas abordagens contextualizadas e proposições referentes às noções de ponto fixo nas principais funções reais (afim, quadrática, modular, dentre outras) e sua interpretação geométrica. São abordados de maneira introdutória os conceitos do teorema do ponto fixo de Brouwer, o teorema do ponto fixo de Banach e o método de resolução de equações por aproximações sucessivas
The main objective of this work is to produce a theoretical concepts related to fixed point, enabling, for high school students, the development of skills and competencies related to Mathematics. This work placed contextualized approaches and proposals relating to notions of fixed point in the main real functions (affine, quadratic, modular, among others) and its geometric interpretation. Are approached introductory concepts of the fixed point theorem of Brouwer's, fixed point theorem of Banach and the method of solving equations by successive approximations
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Lafforgue, Vincent. "K-theorie bivariante pour les algebres de banach et conjecture de baum-connes." Paris 11, 1999. http://www.theses.fr/1999PA112062.
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Je suis parvenu dans ma these a construire une k-theorie bivariante pour les algebres de banach. Cela m'a permis de demontrer la conjecture de baum-connes pour les groupes de lie semi-simples et les groupes reductifs p-adiques, ainsi que pour les sous-groupes discrets de type fini de sl#3(f), avec f une extension finie de q#p et pour les sous-groupes discrets cocompacts de sp(n, 1), sl#3(r) et sl#3(c). J'ai aussi demontre une conjecture analogue a la conjecture de baum-connes pour les algebres l#1 (et plus generalement toutes les bonnes completions) des sous-groupes fermes des groupes de lie semi-simples et des groupes reductifs p-adiques.
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Ali, Abdullah Khalifa Saeed. "Some topics in the theory of Banach function algebras." Thesis, University of Nottingham, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338490.
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Zuick, Nhan H. "The Gelfand Theorem for Commutative Banach Algebras." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/243.
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We give an overview of the basic properties of Banach Algebras. After that we specialize to the case of commutative Banach Algebras and study the Gelfand Map. We study the main characteristic of that map, and work on some applications.
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Rogozhin, Alexander. "Approximation Methods for Two Classes of Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200300091.
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The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigatedDie Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren
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Magill, Matthew. "Topological K-theory and Bott Periodicity." Thesis, Uppsala universitet, Algebra och geometri, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-322927.
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Panova, Olga. "Real Gelfand-Mazur algebras /." Online version, 2006. http://dspace.utlib.ee/dspace/bitstream/10062/117/1/panovaolga.pdf.
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Hazrat, Roozbeh. "On K-theory of classical-like groups." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=969899742.
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Schadeck, Laurent. "On the K-theory of tame Artim stacks." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85745.
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This thesis pertains to the algebraic K-theory of tame Artin stacks. Building on earlier work of Vezzosi and Vistoli in equivariant K-theory, which we translate in stacky language, we give a description of the algebraic K-groups of tame quotient stacks. Using a strategy of Vistoli, we recover Grothendieck-Riemann-Roch-like formulae for tame quotient stacks that refine Toën’s
Grothendieck-Riemann-Roch formula for Deligne-Mumford stacks (as it was realized that the latter pertains to quotient stacks since it relies on the resolution property). Our formulae differ from Toën’s in that, instead of using the standard inertia stack, we use the cyclotomic inertia stack introduced by Abramovich, Graber and Vistoli in the early 2000s. Our results involve the rational part of the K'-theory of the object considered. We establish a few conjectures, the main one (Conjecture 6.3) pertaining to the covariance of our Lefschetz-Riemann-Roch map for proper morphisms of tame stacks (not necessarily representable). Other future works might be dedicated to the study of torsion in K'-groups as well as more general Artin stacks.
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Melo, S. T., R. Nest, and Elmar Schrohe. "C*-structure and K-theory of Boutet de Monvel's algebra." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2616/.
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We consider the norm closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold X with boundary ∂X. We first describe the image and the kernel of the continuous extension of the boundary principal symbol homomorphism to A. If X is connected and ∂X is not empty, we then show that the K-groups of A are topologically determined. In case the manifold, its boundary, and the cotangent space of its interior have torsion free K-theory, we get Ki(A,k) congruent Ki(C(X))⊕Ksub(1-i)(Csub(0)(T*X)),i = 0,1, with k denoting the compact ideal, and T*X denoting the cotangent bundle of the interior. Using Boutet de Monvel's index theorem, we also prove that the above formula holds for i = 1 even without this torsion-free hypothesis. For the case of orientable, two-dimensional X, Ksub(0)(A) congruent Z up(2g+m) and Ksub(1)(A) congruent Z up(2g+m-1), where g is the genus of X and m is the number of connected components of ∂X. We also obtain a composition sequence 0 ⊂ k ⊂ G ⊂ A, with A/G commutative and G/k isomorphic to the algebra of all continuous functions on the cosphere bundle of ∂X with values
in compact operators on L²(R+).
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Rogozhin, Alexander. "Approximation methods for two classes of singular integral equations." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=968783279.
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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Greenfield, David. "Semigroup representations : an abstract approach." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:ebe5ecaf-e400-41de-bcd2-e168475ac76e.
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Chapter One After the definitions and basic results required for the rest of the thesis, a notion of spectrum for semigroup representations is introduced and some relevant examples given. Chapter Two Any semigroup representation by isometries on a Banach space may be dilated to a group representation on a larger Banach space. A new proof of this result is presented here, and a connection is shown to exist between the dilation and the trajectories of the dual representation. The problem of dilating various types of spaces, including partially ordered spaces, C*-algebras, and reflexive spaces, is discussed, and new dilation theorems are given for dual Banach spaces and von Neumann algebras. Chapter Three In this chapter the spectrum of a representation is examined more closely with the aid of methods from Banach algebra theory. In the case where the representation is by isometries it is shown that the spectrum is non-empty, that it is compact if and only if the representation is norm-continuous, and that any isolated point in the unitary spectrum is an eigenvalue. Chapter Four An analytic characterisation is given of the spectral conditions that imply a representation by isometries is invertible. For representations of Z+n this con- dition is shown to be equivalent to polynomial convexity. Some topological conditions on the spectrum are also shown to imply invertibility. Chapter Five The ideas of the previous chapters are applied to problems of asymptotic behaviour. Asymptotic stability is described in terms of the behaviour of the dual of a representation. Finally, the case when the unitary spectrum is countable is discussed in detail.
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Mirmohades, Djalal. "N-complexes and Categorification." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-260111.
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This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. Paper I: We study a set of homology functors indexed by positive integers a and b and their corresponding derived categories. We show that there is an optimal subcategory in the domain of every functor given by N-complexes with N = a + b. Paper II: In this paper we show that the lax nerve of the category of chain complexes is pointwise adjoint equivalent to the décalage of the simplicial category of N-complexes. This reveals additional simplicial structure on the lax nerve of the category of chain complexes which provides a categorfication of the triangulated homotopy category of chain complexes. We study this in general and present evidence that the axioms of triangulated categories have a simplicial origin. Paper III: Let n be a product of two distinct prime numbers. We construct a triangulated monoidal category having a Grothendieck ring isomorphic to the ring of n:th cyclotomic integers.
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Junod, Fabien. "Unstable Adams operations on ρ-local compact groups." Thesis, University of Aberdeen, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.531931.
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Let G be any compact connected Lie group and let T ≤ G be a maximal torus. Then for any unstable Adams operation f of degree k, the following diagram commutes up to homotopy «!» And conversely, any map f that makes the above diagram commute must be an unstable Adams operation. Using this characterization, we will construct a self-map of a p-local compact group (S,F,L) in order to define unstable Adams operations on a more general setting. THEOREM. For any p-local compact group (S,F,L) there is a self-equivalence such that the map on the objects when restricted to the identity component of S is a qm-th power map.
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Ditsche, Jochen. "Pseudodifferential analysis in Y*-algebras [psi*-algebras] on transmission spaces, infinite solving ideal chains and K-theory for conformally compact spaces." Aachen Shaker, 2008. http://d-nb.info/988688409/04.
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Corwin, Stephen P. "Representation theory of the diagram An over the ring k[[x]]." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/50001.
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Fix R = k[[x]]. Let Qn be the category whose objects are ((M₁,...,Mn),(f₁,...,fn-1)) where each Mi is a free R-module and fi:Mi⟶Mi+1 for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let βn be the full subcategory of Ωn in which each map fi is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ωn⟶βn. If X is an object of βn, we say that X diagonalizes if X is isomorphic to a direct sum of objects ((M₁,...,Mn),(f₁,...,fn-1)) in which each Mi is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of βn, and which fails only in case X is not diagonalizable.
Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable.Ph. D.
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Csige, Tamás. "K-theoretic methods in the representation theory of p-adic analytic groups." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2017. http://dx.doi.org/10.18452/17697.
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Sei G eine p-adische analytische gruppe, welche die direkte Summe einer torsionfreien p-adische analytische gruppe H mit zerfallender halbeinfacher Liealgebra und einer n-dimensionalen abelschen p-adische analytische gruppe Z ist. In Kapitel 3 zeigen wir folgenden Satz: Sei M ein endlich erzeugter Torsionmodul über der Iwasawaalgebra von G, welcher keine nichtrivialen pseudo-null-Untermoduln besitzt. Dann ist q(M), das Bild von M in der Quotientenkategorie Q, genau dann volltreu, wenn M als Modul über der Iwasawaalgebra von Z torsionsfrei ist. Hierbei bezeichne Q den Serre-Quotienten der Kategorie der Moduln über der Iwasawaalgebra von G nach der Serre-Unterkategorie der pseudo-null-Moduln. In Kapitel 4 zeigen wir folgenden Satz: Es bezeichne T die Kategorie, deren Objekte die endlich erzeugten Modulen über der Iwasawaalgebra von G sind, welche auch als Moduln über der Iwasawaalgebra von H endlich erzeugt sind. Seien M, N zwei Objekte von T. Wir nehmen an, dass M, N keine nichttrivialen pseudo-null-Untermoduln besitzen und q(M) in Q volltreu ist. Dann gilt: Ist [M]=[N] in der Grothendieckgruppe von Q, so ist das Bild von N ebenfalls volltreu. In Kapitel 5 zeugen wir folgenden Satz: Sei G eine beliebige p-adische analytische Gruppe, welche keine Element der Ordung p besitzt. Dann sind die Grothendieckgruppen der Algebra stetiger Distributionen und der Algebra beschränkter Distributionen isomorph zu c Kopien des Rings der ganzen Zahlen, wobei c die Anzahl der p-regulären Konjugationsklassen des Quotienten von G nach einer offenen uniformen pro-p-Untergruppe H bezeichnet.Let G be a compact p-adic analytic group with no element of order p such that it is the direct sum of a torsion free compact p-adic analytic group H whose Lie algebra is split semisimple and an abelian p-adic analytic group Z of dimension n. In chapter 3, we show that if M is a finitely generated torsion module over the Iwasawa algebra of G with no non-zero pseudo-null submodule, then the image q(M) of M via the quotient functor q is completely faithful if and only if M is torsion free over the Iwasawa algebra of Z. Here the quotient functor q is the unique functor from the category of modules over the Iwasawa algebra of G to the quotient category with respect to the Serre subcategory of pseudo-null modules. In chapter 4, we show the following: Let M, N be two finitely generated modules over the Iwasawa algebra of G such that they are objects of the category Q of those finitely generated modules over the Iwasaw algebra of G which are also finitely generated as modules over the Iwasawa algebra of H. Assume that q(M) is completely faithful and [M] =[N] in the Grothendieck group of Q. Then q(N) is also completely faithful. In chapter 6, we show that if G is any compact p-adic analytic group with no element of order p, then the Grothendieck groups of the algebras of continuous distributions and bounded distributions are isomorphic to c copies of the ring of integers where c denotes the number of p-regular conjugacy classes in the quotient group of G with an open normal uniform pro-p subgroup H of G.
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Germano, Geilson Ferreira. "Uma Introdução a Álgebras de Banach e C*- Álgebras." Master's thesis, Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/9813.
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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In this dissertation we develop a rst contact with the theory of Banach Algebras and C*-algebras. As usual of a rst contact, we build the Spectral Theory in Banach algebras with unit. We present the characterization theorems of C *-algebras of Gelfand-Naimark and Gelfand-Naimark-Segal, including the GNS construction. Moreover, we prove a theorem which characterizes all complex homomorphisms in the C*-algebra C(X), as point-evaluation homomorphisms. We also present, as a curiosity, a proof of the Fundamental Theorem of Algebra using the Gelfand-Mazur Theorem. As a prerequisite to the Gelfand-Naimark-Segal's characterization of C *-algebras, we further develop, in the background, the theory of the direct sum of any family of Hilbert spaces. .
Nesta dissertação desenvolveremos um primeiro contato com a Teoria de Álgebras de Banach e C*-álgebras. Como tópico de um primeiro contato, construiremos a Teoria Espectral em Álgebras de Banach com unidade. Apresentaremos os Teoremas de Caracterização de C*-álgebras de Gelfand-Naimark, e Gelfand-Naimark-Segal, incluindo a constru c~ao GNS. Al em disso, provamos um teorema que caracteriza todos os homomor smos complexos na C*-álgebra C(X) como sendo homomor smos de avaliação. Apresentaremos também, como curiosidade, uma prova do Teorema Fundamental da Álgebra a partir do Teorema de Gelfand-Mazur. Como um pré requisito a Caracterização de Gelfand-Naimark-Segal de C*-álgebras, desenvolvemos ainda, em segundo plano, a teoria da soma direta de uma familia qualquer de espaços de Hilbert.
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Pallekonda, Seshendra. "Bounded category of an exact category." Diss., Online access via UMI:, 2008.
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Bradley, Paul Michael. "Counting G-orbits on the induced action on k-subsets." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/counting-gorbits-on-the-induced-action-on-ksubsets(bd41f2da-eb59-4a6b-bf58-84954ccb9621).html.
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Let G be a finite permutation group acting on a finite set Ω. Then we denote by σk(G,Ω) the number of G-orbits on the set Ωk, consisting of all k-subsets of Ω. In this thesis we develop methods for calculating the values for σk(G,Ω) and produce formulae for the cases that G is a doubly-transitive simple rank one Lie type group. That is G ∼ = PSL(2,q),Sz(q),PSU(3,q) or R(q). We also give reduced functions for the calculation of the number of orbits of these groups when k = 3 and go on to consider the numbers of orbits, when G is a finite abelian group in its regular representation. We then consider orbit lengths and examine groups with “large” G-orbits on subsetsof size 3.
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Kallus, Paul Peter [Verfasser], Etienne [Akademischer Betreuer] Emmich, Karl-Heinz [Akademischer Betreuer] Förster, Jussi [Gutachter] Berndt, and Bela [Gutachter] Nagy. "Semi-monic operator functions : Perron-Frobenius theory, factorization in ordered Banach algebras and degree-reductions / Paul Peter Kallus ; Gutachter: Jussi Berndt, Bela Nagy ; Etienne Emmich, Karl-Heinz Förster." Berlin : Technische Universität Berlin, 2016. http://d-nb.info/1156013046/34.
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Mertsch, Darvin Verfasser], Konrad [Akademischer Betreuer] [Waldorf, Konrad Gutachter] Waldorf, Thomas [Gutachter] Schick, and Eckhard [Gutachter] [Meinrenken. "Geometric Models of Twisted K-Theory based Bundle Gerbes and Algebra Bundles / Darvin Mertsch ; Gutachter: Konrad Waldorf, Thomas Schick, Eckhard Meinrenken ; Betreuer: Konrad Waldorf." Greifswald : Universität Greifswald, 2020. http://nbn-resolving.de/urn:nbn:de:gbv:9-opus-40972.
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Mertsch, Darvin [Verfasser], Konrad [Akademischer Betreuer] Waldorf, Konrad [Gutachter] Waldorf, Thomas [Gutachter] Schick, and Eckhard [Gutachter] Meinrenken. "Geometric Models of Twisted K-Theory based Bundle Gerbes and Algebra Bundles / Darvin Mertsch ; Gutachter: Konrad Waldorf, Thomas Schick, Eckhard Meinrenken ; Betreuer: Konrad Waldorf." Greifswald : Universität Greifswald, 2020. http://d-nb.info/1222161834/34.
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Mathew, Panakkal J. "Three Topics in Analysis: (I) The Fundamental Theorem of Calculus Implies that of Algebra, (II) Mini Sums for the Riesz Representing Measure, and (III) Holomorphic Domination and Complex Banach Manifolds Similar to Stein Manifolds." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_diss/2.
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We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds that is similar in nature and definition to the class of Stein manifolds.
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Bosa, Puigredon Joan. "Continuous fields of c-algebras, their cuntz semigroup and the geometry of dimension fuctions." Doctoral thesis, Universitat Autònoma de Barcelona, 2013. http://hdl.handle.net/10803/126516.
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Aquesta tesi doctoral tracta sobre C*-àlgebres i els seus invariants de Teoria K. Ens hem centrat principalment en l’estructura d’una classe de C*-àlgebres anomenada camps continus i l’estudi d’un dels seus invariants: el semigrup de Cuntz. Més concretament, analitzem el següent: (1)- Estructura dels camps continus : A la literatura hi ha dos exemples que donen una idea clara sobre la complexitat dels camps continus de C*-àlgebres. El primer va ser construït per M. Dadarlat i G. A. Elliott al 2007 i és un camp continu A sobre l’interval unitat amb fibres mútuament isomorfes, Teoria K no finitament generada i que no és localment trivial enlloc. El segon exemple mostra que, fins i tot quan la Teoria K de les fibres s’anul·la, el camp pot ser no trivial enlloc si l’espai base té dimensió infinita (Dadarlat, 2009). Veient aquests exemples és natural preguntar-se quina és l’estructura dels camps continus d’àlgebres de Kirchberg sobre un espai de dimensió finita, amb fibres mútuament isomorfes i Teoria K finitament generada. Tractem aquesta qüestió al Capítol 2 de la memòria. (2)- El semigrup de Cuntz de camps continus : Per a C*-àlgebres de dimensió baixa sense obstruccions cohomològiques, una descripció del seu semigrup de Cuntz, a través d’avaluació puntual, s’ha obtingut en termes de funcions semicontínues sobre l’expectre que prenen valors en els enters positius estesos (Robert, 2009). Per camps més generals la clau està en descriure l’aplicació següent: _: Cu(A) ! Q x2X Cu(Ax) donada per _hai = (ha(x)i)x2X; on Cu(Ax) és el semigrup de Cuntz de la fibra Ax. En el Capítol 3 de la memòria, l’aplicació _ s’estudia en el cas que X tingui dimensió petita i totes les fibres de la C(X)-àlgebra A no són necessàriament isomorfes entre sí. Més concretament, demostrem que és possible recuperar el semigrup de Cuntz d’una classe adequada de camps continus com el semigrup de seccions globals de tx2XCu(Ax) a X. Això s’utilitza posteriorment per reescriure un resultat de classificació degut a Dadarlat, Elliott i Niu (2012) utilitzant un sol invariant en comptes d’un feix de grups. (3)-Funcions de dimensió en una C*-algebra : L’estudi de funcions de dimensió va ser iniciat per Cuntz a 1978, i desenvolupat posteriorment per Blackadar i Handelman al 1982. En el seu article van aparèixer dues preguntes naturals: decidir si l’espai afí de funcions de dimensió és un símplex, i si també el conjunt de funcions de dimensió semicontínues inferiorment és dens a l’espai de totes les funcions de dimensió. En el Capítol 4 calculem el rang estable d’algunes classes de camps continus i això ens ajuda a provar que les dues conjectures anteriors tenen resposta afirmativa per camps continus A sobre espais de dimensió 1 i amb hipòtesis febles en les seves fibres.This thesis deals with C*-algebras and their K-theoretical invariants. We have mainly focused on the structure of a class of C*-algebras called continuous fields, and the study of one of its invariants, the Cuntz semigroup. More concretely, we analyse the following: (1)-Structure of Continuous Fields of C*-algebras : In the literature there are two examples which clearly give an idea about the complexity of continuous field C*-algebras. The first one was constructed by M. Dadarlat and G. A. Elliott in 2007, and it is a continuous field C*- algebra A over the unit interval with mutually isomorphic fibers, with non-finitely generated K-theory and such that it is nowhere locally trivial. The second example shows that, even if the K-theory of the fibers vanish, the field can be nowhere locally trivial if the base space is infinite-dimensional (Dadarlat, 2009). From the above examples, it is natural to ask which is the structure of continuous fields of Kirchberg algebras over a finite-dimensional space with mutually isomorphic fibers and finitely generated K-theory. This question has been adressed in Chapter 2 of the memoir. (2)-The Cuntz semigroup of continuous field C*-algebras : For commutative C*-algebras of lower dimension where there are no cohomological obstructions, a description of their Cuntz semigroup via point evaluation has been obtained in terms of (extended) integer valued lower semicontinuous functions on their spectrum (Robert, 2009). For more general continuous fields, the key is to describe the map : Cu(A) ! Q x2X Cu(Ax) given by hai = (ha(x)i)x2X; where Cu(Ax) is the Cuntz semigroup of the fiber Ax. In Chapter 3 of the memoir, the map is studied in the case when X has low dimension and all the fibers of the C(X)-algebra A are not necessarily mutually isomorphic. Concretely, we prove that it is possible to recover the Cuntz semigroup of a suitable class of continuous fields as the semigroup of global sections of tx2XCu(Ax) to X. This is further used to rephrase a classification result by Dadarlat, Elliott and Niu (2012) by using a single invariant instead of a sheaf of groups. (3)-Dimension Functions on a C*-algebra : The study of dimension functions on C -algebras was started by Cuntz in 1978, and further developed by B. Blackadar and D. Handelman in 1982. In the latter article, two natural questions arised: to decide whether the affine space of dimension functions is a simplex, and also whether the set of lower semicontinuous dimension functions is dense in the space of all dimension functions. In Chapter 4 we compute the stable rank of some class of continuous field C*-algebras, which helps us to move on to show that the above two conjectures have affirmative answers for continuous fields A over one-dimensional spaces and with mild assumptions on their fibers.
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Francis, Amanda. "New Computational Techniques in FJRW Theory with Applications to Landau Ginzburg Mirror Symmetry." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3265.
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Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. In the Landau-Ginzburg setting, we have two constructions, the A and B models, which are created based on a choice of an affine singularity with a group of symmetries. Both models are vector spaces equipped with multiplication and a pairing (making them Frobenius algebras), and they are also Frobenius manifolds. We give a result relating stabilization of singularities in classical singularity to its counterpart in the Landau-Ginzburg setting. The A model comes from so-called FJRW theory and can be de fined up to a full cohomological field theory. The structure of this model is determined by a generating function which requires the calculation of certain numbers, which we call correlators. In some cases the their values can be computed using known techniques. Often, there is no known method for finding their values. We give new computational methods for computing concave correlators, including a formula for concave genus-zero, four-point correlators and show how to extend these results to find other correlator values. In many cases these new methods give enough information to compute the A model structure up to the level of Frobenius manifold. We give the FJRW Frobenius manifold structure for various choices of singularities and groups.
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Nguyen, Le Chi Quyet. "Une description fonctorielle des K-théories de Morava des 2-groupes abéliens élémentaires." Thesis, Angers, 2017. http://www.theses.fr/2017ANGE0032/document.
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Le but de cette thèse est l'étude, d'un point de vue fonctoriel, des K-théories de Morava modulo 2 des 2-groupes abéliens élémentaires. Autrement dit, nous étudions les foncteurs covariants $V \mapsto K(n)^*(BV^{\sharp})$ pour le premier p=2 et n un entier positif.Le cas n=1, qui résulte directement du travail d'Atiyah sur la K-théorie topologique, nous donne un foncteur coanalytique qui ne possède aucun sous-foncteur polynomial non-constant. Il est très différent du cas n>1, où les foncteurs mentionnés ci-dessus s'avèrent être analytiques.La théorie de Henn-Lannes-Schwartz fournit une correspondance entre les foncteurs analytiques et les modules instables sur l'algèbre de Steenrod. Nous déterminons le module instable correspondant au foncteur analytique $V \mapsto K(2)^*(BV^{\sharp})$, en étudiant la relation entre ce foncteur et la structure d'anneau de Hopf de l'homologie de l'omega-spectre associé à la théorie K(2)The aim of this PhD thesis is to study, from a functorial point of view, the mod 2 Morava K-theories of elementary abelian 2-groups. Namely, we study the covariant functors $V \mapsto K(n)^*(BV^{\sharp})$ for the prime p=2 and n a positive integer.The case n=1, which follows directly from the work of Atiyah on topological K-theory, gives us a coanalytic functor which contains no non-constant polynomial sub-functor. This is very different from the case n>1, where the above-mentioned functors are analytic.The theory of Henn-Lannes-Schwartz provides a correspondence between analytic functors and unstable modules over the Steenrod algebra. We determine the unstable module corresponding to the analytic functor $V \mapsto K(2)^*(BV^{\sharp})$, by studying the relation between this functor and the Hopf ring structure of the homology of the omega-spectrum associated to the theory K(2)
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Fernández, Juan Francisco Camasca. "Algumas aplicações de combinatória infinita a espaços de funções contínuas." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27072017-164022/.
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O principal objetivo deste trabalho é estudar diversas aplicações de combinatória infinita em espaços de funções contínuas, definidas em espaços compactos Hausdorff. Usando combinatória infinita para uma álgebra de Boole, por meio da dualidade de Stone, obtemos um espaço compacto Hausdorff. Com certas propriedades na álgebra de Boole é possível analisar propriedades analíticas no espaço de funções contínuas definidas em tal espaço. Especificamente, analisamos a propriedade de Grothendieck. Também analisamos a relação entre o espaço de funções contínuas e o espaço compacto Hausdorff sobre o qual é definido. Apresentamos um resultado que permite obter diversos resultados conhecidos de uma maneira uniforme (só usando fatos de topologia e teoria de conjuntos), dotando o espaço de funções contínuas de uma ordem peculiar. Finalmente, estudamos um pouco de jogos topológicos mediante diversos exemplos.The main purpose of this work is to study some infinite combinatorics applications in spaces of continuous functions, defined in Hausdorff compact spaces. Using infinite combinatorics in Boolean algebras, through Stone duality, we obtain a compact Hausdorff space. With certain properties in Boolean algebras it is possible to analyze analytic properties in the space of continuous functions defined in such space. Specifically, we analyze the Grothendieck property. We also analyze the relationship between the space of continuous functions and the compact Hausdorff space on which it is defined. We present a result that allows to obtain several known results in a uniform way (only using facts of topology and set theory), giving the space of continuous functions a peculiar order. Finally, we study some topological games through several examples.
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GOLENIA, Sylvain. "Méthodes algébriques dans l'analyse spectrale d'opérateurs sur les graphes et les variétés." Phd thesis, Université de Cergy Pontoise, 2004. http://tel.archives-ouvertes.fr/tel-00008539.
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Dans cette these, produit de techniques issues de la theorie des $C^*$-algebres et de la theorie spectrale, nous etablissons de nouveaux resultats concernant les proprietes spectrales d'operateurs agissant sur les arbres et divers criteres concernant la stabilite du spectre essentiel d'operateurs non-bornes.Elle se compose de trois articles.
Les deux premiers traitent de la theorie spectrale et de la diffusion des operateurs de Schroedinger sur un arbre et de sa generalisation naturelle aux espaces de Fock. Les problemes abordes sont : la validite de l'estimation de Mourre et la caracterisation du spectre essentiel d'operateurs anisotropes par des methodes $C^*$-algebriques.
Dans le troisieme article, nous nous proposons une recherche de criteres de stabilite du spectre essentiel pour des operateurs agissant sur des modules de Banach. Les applications couvrent les operateurs de Dirac, les perturbations de metriques riemanniennes, les operateurs sous forme divergence et bien d'autres. Outre son formalisme algebrique, ce travail est caracterise par l'absence de conditions de regularite dans les hypotheses.
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Lebed, Victoria. "Objets tressés : une étude unificatrice de structures algébriques et une catégorification des tresses virtuelles." Phd thesis, Université Paris-Diderot - Paris VII, 2012. http://tel.archives-ouvertes.fr/tel-00775857.
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Dans cette thèse on développe une théorie générale des objets tressés et on l'applique à une étude de structures algébriques et topologiques. La partie I contient une théorie homologique des espaces vectoriels tressés et modules tressés, basée sur le coproduit de battage quantique. La construction d'un tressage structurel qui caractérise diverses structures - auto-distributives (AD), associatives, de Leibniz - permet de généraliser et unifier des homologies familières. Les hyper-bords de Loday, ainsi que certaines opérations homologiques, apparaissent naturellement dans cette interprétation. On présente ensuite des concepts de système tressé et module multi-tressé. Appliquée aux bigèbres, bimodules, produits croisés et (bi)modules de Hopf et de Yetter-Drinfel'd, cette théorie donne leurs interprétations tressées, homologies et actions adjointes. La no- tion de produits tensoriels multi-tressés d'algèbres donne un cadre unificateur pour les doubles de Heisenberg et Drinfel'd, ainsi que les algèbres X de Cibils-Rosso et Y et Z de Panaite. La partie III est orientée vers la topologie. On propose une catégorification des groupes de tresses virtuelles en termes d'objets tressés dans une catégorie symétrique (CS). Cette approche de double tressage donne une source de représentations de V Bn et un traitement catégorique des racks virtuels de Manturov et de la représentation de Burau tordue. On définit ensuite des structures AD dans une CS arbitraire et on les munit d'un tressage. Les techniques tressées de la partie I amènent alors à une théorie homologique des structures AD catégoriques. Les algèbres associatives, de Leibniz et de Hopf rentrent dans ce cadre catégorique.
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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, 2011. https://monarch.qucosa.de/id/qucosa%3A19670.
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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt.
Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet.
Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Cedeño, Ariel Blanco. "On weak amenability of the algebra of approximable operators." Phd thesis, 2001. http://hdl.handle.net/1885/148066.
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Bapela, Manas Majakwane. "Riesz theory and Fredholm determinants in Banach algebras." Thesis, 1999. http://hdl.handle.net/2263/30088.
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In the classical theory of operators on a Banach space a beautiful interplay exists between Riesz and Fredholm theory, and the theory of traces and de¬terminants for operator ideals. In this thesis we obtain a complete Riesz de¬composition theorem for Riesz elements in a semi prime Banach algebra and on the other hand extend the existing theory of traces and determinants to a more general setting of Banach algebras. In order to obtain some of these results we use the notion of finite multiplicity of spectral points to give a characterization of the essential spec¬trum for elements in a Banach algebra. As an immediate corollary we obtain the well-known characterization of Riesz elements namely that their non-zero spectral points are isolated and of finite multiplicities. In the final chapter of the thesis we use Plemelj's type formulas to define a determinant on the ideal of finite rank elements and show that it extends continuously to the ideal of nuclear elements.Thesis (PhD (Mathematics))--University of Pretoria, 2006.
Mathematics and Applied Mathematics
unrestricted
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Braatvedt, Gareth. "Characterizations of scalars in Banach algebras." Thesis, 2011. http://hdl.handle.net/10210/3704.
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Moolman, Ruan. "On the role of subharmonic functions in the spectral theory of general Banach algebras." Thesis, 2010. http://hdl.handle.net/10210/3026.
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Vermaak, Jacobus Andries. "Riesz- en Fredholmteorie in Banach-algebras." Thesis, 2014. http://hdl.handle.net/10210/12031.
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Smit, Joukje Anneke. "Koliha–Drazin invertibles form a regularity." Diss., 2010. http://hdl.handle.net/10500/4905.
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The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms
are satisfied. However, there arise a number of spectra, usually defined for a single element
of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and
V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was
to describe the underlying set of elements on which the spectrum is defined. The axioms of a
regularity provide important consequences. We prove that the set of Koliha-Drazin invertible
elements, which includes the Drazin invertible elements, forms a regularity. The properties of
the spectrum corresponding to a regularity are also investigated.Mathematical Sciences
M. Sc. (Mathematics)
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Bharucha, Pourus. "Amenability properties and their consequences in Banach algebras." Phd thesis, 2008. http://hdl.handle.net/1885/150131.
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Athar, Tazeen [Verfasser]. "Local spectral methods in the theory of Banach function algebras / by Tazeen Athar." 2010. http://d-nb.info/1009514520/34.
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Paravicini, Walther Dietrich [Verfasser]. "KK-theory for Banach algebras and proper groupoids / vorgelegt von Walther Dietrich Paravicini." 2006. http://d-nb.info/983108315/34.
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"Derivations mapping into the radical." Thesis, 2010. http://hdl.handle.net/10210/3274.
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M.Sc.One of the earliest results (1955) in the theory of derivations is the celebrated theorem of I. M. Singer and J. Wermer [14] which asserts that every bounded derivation on a commutative Banach algebra has range contained in the radical. However, they immediately conjectured that their result will still hold if the boundedness condition was dropped. This conjecture of Singer and Wermer was confirmed only in 1988, by M. P. Thomas [23], when he showed that every derivation (bounded or unbounded) on a commutative Banach algebra has range contained in the radical. But it is not known whether an analogue of the Kleinecke-Shirokov Theorem holds for everywhere defined unbounded derivation.