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Опубліковано: 15 грудня 2023

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Статті в журналах з теми "K-theory of banach algebra"

1

PHILLIPS, N. CHRISTOPHER. "K-THEORY FOR FRÉCHET ALGEBRAS." International Journal of Mathematics 02, no. 01 (February 1991): 77–129. http://dx.doi.org/10.1142/s0129167x91000077.

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Анотація:
We define K-theory for Fréchet algebras (assumed to be locally multiplicatively convex) so as to simultaneously generalize K-theory for σ-C*-algebras and K-theory for Banach algebras. The main results on K-theory of σ-C*-algebras, which are analogs of standard theorems on representable K-theory of spaces, carry over to the more general case. Our theory also gives the expected results in two other cases. If the invertible elements of a Fréchet algebra are an open set, as is the case for dense subalgebras of C*-algebras closed under holomorphic functional calculus, then our theory agrees with the result of applying the Banach algebra definition. For commutative unital Fréchet algebras, our K-theory is the same as the representable K-theory of the maximal ideal space with its compactly generated topology.
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2

Martinez-Moreno, J., and A. Rodriguez-Palacios. "Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups." Proceedings of the Edinburgh Mathematical Society 28, no. 1 (February 1985): 91–95. http://dx.doi.org/10.1017/s0013091500003229.

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If a is an element of a complex unital Banach algebra whose numerical range is confined to a closed angular region with vertex at zero and angle strictly less than π, we imbed a in a holomorphic semigroup with parameter in the open right half plane.There has been recently a great development in the theory of semigroups in Banach algebras (see [6]), with attention focused on the relation between the structure of a given Banach algebra and the existence of continuous or holomorphic non-trivial semigroups with certain properties with range in this algebra. The interest of this paper arises from the fact that we relate in it, we think for the first time, this new point of view in the theory of Banach algebras with the already classic one of numerical ranges [2,3]. The proofs of our results use, in addition to some basic ideas from numerical ranges in Banach algebras, the concept of extremal algebra Ea(K) of a compact convex set K in ℂ due to Bollobas [1] and concretely the realization of Ea(K) achieved by Crabb, Duncan and McGregor [4].
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3

Gourdeau, Frédéric. "Amenability of Banach algebras." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 2 (March 1989): 351–55. http://dx.doi.org/10.1017/s0305004100067840.

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We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1].
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4

Hadwin, Don, and Mehmet Orhon. "A noncommutative theory of Bade functionals." Glasgow Mathematical Journal 33, no. 1 (January 1991): 73–81. http://dx.doi.org/10.1017/s0017089500008053.

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Анотація:
Since the pioneering work of W. G. Bade [3, 4] a great deal of work has been done on bounded Boolean algebras of projections on a Banach space ([11, XVII.3.XVIII.3], [21, V.3], [16], [6], [12], [13], [14], ]17], [18], [23], [24]). Via the Stone representation space of the Boolean algebra, the theory can be studied through Banach modules over C(K), where K is a compact Hausdorff space. One of the key concepts in the theory is the notion of Bade functionals. If X is a Banach C(K)-module and x ε X, then a Bade functional of x with respect to C(K) is a continuous linear functional α on X such that, for each a in C(K) with a ≥ 0, we have(i) α (ax) ≥0,(ii) if α (ax) = 0, then ax = 0.
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5

Kubota, Yosuke. "Notes on twisted equivariant K-theory for C*-algebras." International Journal of Mathematics 27, no. 06 (June 2016): 1650058. http://dx.doi.org/10.1142/s0129167x16500580.

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Анотація:
In this paper, we study a generalization of twisted (groupoid) equivariant K-theory in the sense of Freed–Moore for [Formula: see text]-graded [Formula: see text]-algebras. It is defined by using Fredholm operators on Hilbert modules with twisted representations. We compare it with another description using odd symmetries, which is a generalization of van Daele’s K-theory for [Formula: see text]-graded Banach algebras. In particular, we obtain a simple presentation of the twisted equivariant K-group when the [Formula: see text]-algebra is trivially graded. It is applied for the bulk-edge correspondence of topological insulators with CT-type symmetries.
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6

Feeman, Timothy G. "The Bourgain algebra of a nest algebra." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (February 1997): 151–66. http://dx.doi.org/10.1017/s0013091500023518.

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In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-order (and higher) Bourgain algebras of a nest algebra, showing for instance that the second-order two-sided Bourgain algebra coincides with the two-sided Bourgain algebra itself in this case.
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7

Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.
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8

Noreldeen, Alaa Hassan. "On the Homology Theory of Operator Algebras." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/368527.

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We investigate the cyclic homology and free resolution effect of a commutative unital Banach algebra. Using the free resolution operator, we define the relative cyclic homology of commutative Banach algebras. Lemmas and theorems of this investigation are studied and proved. Finally, the relation between cyclic homology and relative cyclic homology of Banach algebra is deduced.
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9

Pfaffenberger, W. E., and J. Phillips. "Commutative Gelfand Theory for Real Banach Algebras: Representations as Sections of Bundles." Canadian Journal of Mathematics 44, no. 2 (April 1, 1992): 342–56. http://dx.doi.org/10.4153/cjm-1992-023-4.

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AbstractWe are concerned here with the development of a more general real case of the classical theorem of Gelfand ([5], 3.1.20), which represents a complex commutative unital Banach algebra as an algebra of continuous functions defined on a compact Hausdorff space.In § 1 we point out that when looking at real algebras there is not always a one-to-one correspondence between the maximal ideals of the algebra B, denoted ℳ, and the set of unital (real) algebra homomorphisms from B into C, denoted by ΦB. This simple point and subsequent observations lead to a theory of representations of real commutative unital Banach algebras where elements are represented as sections of a bundle of real fields associated with the algebra (Theorem 3.5). After establishing this representation theorem, we look into the question of when a real commutative Banach algebra is already complex. There is a natural topological obstruction which we delineate. Theorem 4.8 gives equivalent conditions which determine whether such an algebra is already complex.Finally, in § 5 we abstractly characterize those section algebras which appear as the target algebras for our Gelfand transform. We dub these algebras “almost complex C*- algebras” and provide a natural classification scheme.
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10

Rupp, R., та A. Sasane. "Reducibility in Aℝ(K), Cℝ(K), and A(K)". Canadian Journal of Mathematics 62, № 3 (1 червня 2010): 646–67. http://dx.doi.org/10.4153/cjm-2010-025-9.

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AbstractLet K denote a compact real symmetric subset of ℂ and let Aℝ(K) denote the real Banach algebra of all real symmetric continuous functions on K that are analytic in the interior K◦ of K, endowed with the supremum norm. We characterize all unimodular pairs ( f , g) in Aℝ(K)2 which are reducible. In addition, for an arbitrary compact K in ℂ, we give a new proof (not relying on Banach algebra theory or elementary stable rank techniques) of the fact that the Bass stable rank of A(K) is 1. Finally, we also characterize all compact real symmetric sets K such that Aℝ(K), respectively Cℝ(K), has Bass stable rank 1.
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Дисертації з теми "K-theory of banach algebra"

1

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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Анотація:
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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2

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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Анотація:
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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3

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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4

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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5

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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6

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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Анотація:
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-Connes
A 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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7

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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Анотація:
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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8

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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9

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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Анотація:
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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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10

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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Анотація:
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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Книги з теми "K-theory of banach algebra"

1

Palmer, Theodore W. Banach algebras and the general theory of *-algebras. Cambridge [England]: Cambridge University Press, 1994.

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2

Palmer, Theodore W. Banach algebras and the general theory of *-algebras. Cambridge: Cambridge University Press, 2001.

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3

Douglas, Ronald G. Banach Algebra Techniques in Operator Theory. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1656-8.

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4

Douglas, Ronald G. Banach algebra techniques in operator theory. 2nd ed. New York: Springer, 1998.

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5

Abramovich, Y. A. Banach C(K)-modules and operators preserving disjointness. Harlow, Essex, England: Longman, 1992.

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6

Harmand, P. M-ideals in Banach spaces and Banach algebras. Berlin: Springer-Verlag, 1993.

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7

Local and analytic cyclic homology. Zürich: European Mathematical Society, 2007.

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8

Perturbations of Banach algebras. Berlin: Springer-Verlag, 1985.

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9

K, Kitover A., ed. Inverses of disjointness preserving operators. Providence, R.I: American Mathematical Society, 2000.

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10

Tomczak-Jaegerman, Nicole. Banach-Mazur distances and finite-dimensional operator ideals. Harlow: Longman Scientific & Technical, 1989.

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Більше джерел

Частини книг з теми "K-theory of banach algebra"

1

Rosenberg, Jonathan. "Comparison Between Algebraic and Topological K-Theory for Banach Algebras and C*-Algebras." In Handbook of K-Theory, 843–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-27855-9_16.

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2

Berdikulov, M. A. "Order Unit Space of Type I n with Banach Ball Property." In Algebra and Operator Theory, 183–86. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5072-9_16.

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3

Bridges, Douglas S., and Robin S. Havea. "Square Roots and Powers in Constructive Banach Algebra Theory." In Lecture Notes in Computer Science, 68–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30870-3_8.

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4

Das, Anupam, and Bipan Hazarika. "Measure of Noncompactness in Banach Algebra and Its Application on Integral Equations of Two Variables." In Advances in Metric Fixed Point Theory and Applications, 311–32. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-6647-3_13.

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5

Aupetit, Bernard. "Banach Algebras." In A Primer on Spectral Theory, 30–68. New York, NY: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4612-3048-9_3.

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6

Kadison, Richard V., and John R. Ringrose. "Banach Algebras." In Fundamentals of the Theory of Operator Algebras, 84–138. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-3212-4_3.

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7

Kadison, Richard, and John Ringrose. "Banach algebras." In Fundamentals of the Theory of Operator Algebras. Volume I, 173–235. Providence, Rhode Island: American Mathematical Society, 1997. http://dx.doi.org/10.1090/gsm/015/03.

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8

Müller, Vladimir. "Banach Algebras." In Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, 1–79. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-7788-6_1.

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9

Krupnik, Naum Yakovlevich. "Banach Algebras with Symbol." In Operator Theory: Advances and Applications, 91–119. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-5463-4_4.

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10

Strung, Karen R. "Banach algebras and spectral theory." In Advanced Courses in Mathematics - CRM Barcelona, 1–13. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47465-2_1.

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Тези доповідей конференцій з теми "K-theory of banach algebra"

1

González, Manuel. "Banach spaces with small Calkin algebras." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-10.

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2

Changping Xiong, Jun Zhu, and Jinping Zhao. "K-stable subsets of extended derivations on Banach algebras." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002508.

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3

Melo, Severino T., Ryszard Nest, and Elmar Schrohe. "K-theory of Boutet de Monvel's algebra." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-10.

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4

Auwalu, Abba, and Ali Denker. "Chatterjea-type fixed point theorem on cone rectangular metric spaces with banach algebras." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040595.

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5

BUNKE, ULRICH, MICHAEL JOACHIM, and STEPHAN STOLZ. "CLASSIFYING SPACES AND SPECTRA REPRESENTING THE K-THEORY OF A GRADED C*-ALGEBRA." In Proceedings of the School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704443_0003.

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