Dissertations / Theses on the topic 'Banach algebra'
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1
Mudau, Leonard Gumani. "Zero divisors in banach algebras." Thesis, University of Limpopo (Medunsa Campus), 2010. http://hdl.handle.net/10386/632.
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Yang, Hongfei. "Properties of Banach function algebras." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/49075/.
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This thesis is devoted to the study of various properties of Banach function algebras. We are particularly interested in the study of antisymmetric decompositions for uniform algebras and regularity of Banach function algebras. We are also interested in the study of Swiss cheese sets, essential uniform algebras and characterisations of C(X) among its subalgebras. The maximal antisymmetric decomposition for uniform algebras is a generalisation of the celebrated Stone-Weierstrass theorem and it is a powerful tool in the study of uniform algebras. However, in the literature, not much attention has been paid to the study of closed antisymmetric subsets. In Section 1.7 we give a characterisation of all the closed antisymmetric subsets for the disc algebra on the unit circle, and we use this characterisation to give a new proof of Wermer’s maximality theorem. Then in Section 4.1 we give characterisations of all the closed antisymmetric subsets for normal uniform algebras on the unit interval or the unit circle. The two types of regularity points, the R-point and the point of regularity, are important concepts in the study of regularity of Banach function algebras. In Section 3.2 we construct two examples of compact plane sets X, such that R(X) has either one R-point while having no points of regularity, or R(X) has one point of continuity while having no R-points. There are the first known examples of natural uniform algebras in the literature which show that R-points and points of continuity can be different. We then use properties of regularity points to study R(X) which is not regular while having no non-trivial Jensen measures. We also use properties of regularity points in Section 4.2 to study small exceptional sets for uniform algebras. In Chapter 2 we study Swiss cheese sets. Our approach is to regard Swiss cheese sets “abstractly”: we study the family of sequences of pairs of numbers, where the numbers represent the centre and radius of discs in the complex plane. We then give a natural topology on the space of abstract Swiss cheeses and give topological proofs of various classicalisation theorems. It is standard that the study of general uniform algebras can be reduced to the study of essential uniform algebras. In Chapter 5 we study methods to construct essential uniform algebras. In particular, we continue to study the method introduced in [26] to show that some more properties are inherited by the constructed essential uniform algebra from the original one. We note that the material in Chapter 2 is joint work with J. Feinstein and S. Morley and is published in [28, 27]. The material in Chapter 3 is joint work with J. Feinstein and is published in [32]. Section 4.2 contains joint work with J. Feinstein.
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Esslamzadeh, Gholam Hossein. "Banach algebra structure and amenability of a class of matrix algebras with applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ29033.pdf.
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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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Das, Bata Krishna. "Quantum stochastic analysis in Banach space and operator space." Thesis, Lancaster University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.660115.
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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.
7
Boos, Lynette J. "Function Algebras on Riemann Surfaces and Banach Spaces." Bowling Green State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1151340555.
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Wimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.
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Calzi, Mattia. "Functional Calculus on Homogeneous Groups." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85740.
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In the first part of the thesis, we consider the following problem.
Let G be a homogeneous group, and let (L_1,...,L_n) be a jointly hypoelliptic commutative finite family of formally self-adjoint, homogeneous, left-invariant differential operators without constant terms.
Then, the operators L_j are essentially self-adjoint as operators on L^2(G) with domain C^infty_c(G), and their closures commute emph{as self-adjoint operators}.
Therefore, one may consider the joint functional calculus associated with the family (L_1,...,L_n).
More precisely, for every bounded Borel measurable function $m$ on $R^n$, the corresponding operator m(L_1,...,L_n) commutes with left translations, so that it admits a unique right convolution kernel K(m).
The so-defined kernel transform K then maps S(R^n) continuously into S(G), and L^2(eta) isometrically into L^2(G) for some uniquely determined positive Radon measure eta on R^n; this latter property can be considered as an analogue of the Plancherel isomorphism.
In addition, K maps L^1(eta) continuously into C_0(G), and this property can be considered as an analogue of the Riemann--Lebesgue lemma.
We focus on the following properties of K:
(RL) if K(m)in L^1(G), then m can be taken in C_0(R^n): this is again an analogue of the Riemann--Lebesgue lemma;
(S) if K(m)in S(G), then m can be taken in S(R^n).
We prove that properties (RL) and (S) are compatible with products, and we characterize the Rockland operators which satisfy property (S) when the underlying group G is abelian.
We then consider the case of 2-step stratified groups, and families whose elements are either sub-Laplacians or vector fields of homogeneous degree 2. In this setting, we prove several sufficient conditions, as well as some necessary ones, for properties (RL) and (S); we even characterize them in some more specific settings.
In addition, we study the case of general (that is, not necessarily homogeneous) sub-Laplacians on 2-step stratified groups, and prove that they always satisfy properties (RL) and (S).
We also prove that, under some mild assumptions, a multiplier m can be taken so as to satisfy Mihlin--Hormander conditions of order infinity if and only if the corresponding kernel K(m) satisfies Calderon--Zygmund conditions of order infinity.
In the second part of the thesis, we present some results which are joint work with T. Bruno.
We fix the standard sub-Laplacian on an H-type group, and consider its heat kernel (p_s)_{s>0}. We provide sharp asymptotic estimates at $infty$ for basically all the derivatives of p_1. Because of the homogeneity of the family (p_s), these estimates can also be considered as short-time asymptotics.
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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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Ronquillo, Rivera Javier Alfredo. "Extremely Amenable Groups and Banach Representations." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520548085599864.
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Wilding, David. "Linear algebra over semirings." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/linear-algebra-over-semirings(1dfe7143-9341-4dd1-a0d1-ab976628442d).html.
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Motivated by results of linear algebra over fields, rings and tropical semirings, we present a systematic way to understand the behaviour of matrices with entries in an arbitrary semiring. We focus on three closely related problems concerning the row and column spaces of matrices. This allows us to isolate and extract common properties that hold for different reasons over different semirings, yet also lets us identify which features of linear algebra are specific to particular types of semiring. For instance, the row and column spaces of a matrix over a field are isomorphic to each others' duals, as well as to each other, but over a tropical semiring only the first of these properties holds in general (this in itself is a surprising fact). Instead of being isomorphic, the row space and column space of a tropical matrix are anti-isomorphic in a certain order-theoretic and algebraic sense. The first problem is to describe the kernels of the row and column spaces of a given matrix. These equivalence relations generalise the orthogonal complement of a set of vectors, and the nature of their equivalence classes is entirely dependent upon the kind of semiring in question. The second, Hahn-Banach type, problem is to decide which linear functionals on row and column spaces of matrices have a linear extension. If they all do, the underlying semiring is called exact, and in this case the row and column spaces of any matrix are isomorphic to each others' duals. The final problem is to explain the connection between the row space and column space of each matrix. Our notion of a conjugation on a semiring accounts for the different possibilities in a unified manner, as it guarantees the existence of bijections between row and column spaces and lets us focus on the peculiarities of those bijections. Our main original contribution is the systematic approach described above, but along the way we establish several new results about exactness of semirings. We give sufficient conditions for a subsemiring of an exact semiring to inherit exactness, and we apply these conditions to show that exactness transfers to finite group semirings. We also show that every Boolean ring is exact. This result is interesting because it allows us to construct a ring which is exact (also known as FP-injective) but not self-injective. Finally, we consider exactness for residuated lattices, showing that every involutive residuated lattice is exact. We end by showing that the residuated lattice of subsets of a finite monoid is exact if and only if the monoid is a group.
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Sunehag, Peter. "Interpolation of Subcouples, New Results and Applications." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3777.
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Machovičová, Tatiana. "Banachovy algebry." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445456.
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By Banach algebra we mean Banach space enriched with a multiplication operation. It is a mathematical structure that is used in the non-periodic homogenization of composite materials. The theory of classical homogenization studies materials assuming the periodicity of the structure. For real materials, the assumption of a periodicity is not enough and is replaced by the so-called an abstract hypothesis based on a concept composed mainly of the spectrum of Banach algebra and Sigma convergence. This theory was introduced in 2004.
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Paredes, Rojas Edu. "Operadores θ-monótonos en espacios de Banach reflexivos." Master's thesis, Universidad Nacional Mayor de San Marcos, 2021. https://hdl.handle.net/20.500.12672/17276.
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En el presente trabajo, se siguen las ideas de [2] para operadores σ-monótonos,
probamos la acotación local de un operador θ-monótono multivaluado en el contexto de los espacios de Banach reflexivos de dimensión infinita con ayuda de las
bifunciones ([11]) y asumiendo la semicontinuidad inferior débil de θp¨, yq. Para
esto mostramos que el uso de funciones multivaluadas es mucho más conveniente
que las funciones en el sentido usual. Por otro lado, cabe resaltar que los operadores θ-monótonos definidos en [32] al ser una generalización de los operadores
uniformemente monótonos, fuertemente monótonos, monótonos en el sentido de
Minty-Browder, ε-monótonos, γ-monótonos, pre-monótonos, σ-monótonos y αmonótonos, todo resultado demostrado para un operador θ-monótono se puede
aplicar directamente a los operadores mencionados. También, utilizando las ideas
de [2], conseguimos hacer una demostración directa para la acotación local de un
operador θ-monótono en Rn
, que fue demostrada de forma indirecta en [32], y
para operadores σ-monótonos demostradas de forma indirecta en [22] y también
de forma directa en [2]. Finalmente, se realiza un algoritmo y varios gráficos en
3D y 2D usando Geogebra para una versión geométrica de los ejemplos obtenidos.
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Martini, Alessio. "Algebras of differential operators on Lie groups and spectral multipliers." Doctoral thesis, Scuola Normale Superiore, 2010. http://hdl.handle.net/11384/85663.
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Let (X, μ) be a measure space, and let L1, . . . ,Ln be (possibly unbounded) selfadjoint
operators on L2(X, μ), which commute strongly pairwise, i.e., which
admit a joint spectral resolution E on Rn. A joint functional calculus is then
defined via spectral integration: for every Borel function m : Rn → C,
m(L) = m(L1, . . . ,Ln) =
∫ Rn m(λ) dE(λ) is a normal operator on L2(X, μ), which is bounded if and only if m - called
the joint spectral multiplier associated to m(L) - is (E-essentially) bounded.
However, the abstract theory of spectral integrals does not tackle the following
problem: to find conditions on the multiplier m ensuring the boundedness of
m(L) on Lp(X, μ) for some p ≠ 2.
We are interested in this problem when the measure space is a connected Lie
group G with a right Haar measure, and L1, . . . ,Ln are left-invariant differential
operators on G. In fact, the question has been studied quite extensively in the
case of a single operator, namely, a sublaplacian or a higher-order analogue.
On the other hand, for multiple operators, only specific classes of groups and
specific choices of operators have been considered in the literature.
Suppose that L1, . . . ,Ln are formally self-adjoint, left-invariant differential
operators on a connected Lie group G, which commute pairwise (as operators
on smooth functions). Under the assumption that the algebra generated by
L1, . . . ,Ln contains a weighted subcoercive operator --- a notion due to [ER98],
including positive elliptic operators, sublaplacians and Rockland operators---we
prove that L1, . . . ,Ln are (essentially) self-adjoint and strongly commuting on
L2(G). Moreover, we perform an abstract study of such a system of operators,
in connection with the algebraic structure and the representation theory of G,
similarly as what is done in the literature for the algebras of differential operators
associated with Gelfand pairs.
Under the additional assumption that G has polynomial volume growth,
weighted L1 estimates are obtained for the convolution kernel of the operator
m(L) corresponding to a compactly supported multiplier m satisfying some
smoothness condition. The order of smoothness which we require on m is related
to the degree of polynomial growth of G. Some techniques are presented,
which allow, for some specific groups and operators, to lower the smoothness
requirement on the multiplier.
In the case G is a homogeneous Lie group and L1, . . . ,Ln are homogeneous
operators, a multiplier theorem of Mihlin-H\"ormander type is proved, extending
the result for a single operator of [Chr91] and [MM90]. Further, a product theory
is developed, by considering several homogeneous groups Gj , each of which with
its own system of operators; a non-conventional use of transference techniques
then yields a multiplier theorem of Marcinkiewicz type, not only on the direct
product of the Gj , but also on other (possibly non-homogeneous) groups, containing
homomorphic images of the Gj . Consequently, for certain non-nilpotent
groups of polynomial growth and for some distinguished sublaplacians, we are
able to improve the general result of [Ale94].
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Pavel, Dimovski. "Translation invariant Banach spaces of distributions and boundary values of integral transform." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2015. https://www.cris.uns.ac.rs/record.jsf?recordId=93767&source=NDLTD&language=en.
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We use common notation ∗ for distribution (Scshwartz), (Mp) (Beurling) i {Mp} (Roumieu) setting. We introduce and study new (ultra) distribution spaces, the test function spaces D∗E and their strong duals D'∗E’*.These spaces generalize the spaces D∗Lq , D'∗Lp , B’* and their weighted versions. The construction of our new (ultra)distribution spaces is based on the analysis of a suitable translation-invariant Banach space of (ultra)distribution E with continuous translation group, which turns out to be a convolution module over the Beurling algebra L1ω, where the weight ω is related to the translation operators on E. The Banach space E’∗ stands for L1ωˇ ∗ E’. We apply our results to the study of the convolution of ultradistributions. The spaces of convolutors O’∗C (Rn) for tempered ultradistributions are analyzed via the duality with respect to the test functionspaces O∗C (Rn), introduced in this thesis. Using the properties of translationinvariantBanach space of ultradistributions E we obtain a full characterization ofthe general convolution of Roumieu ultradistributions via the space of integrableultradistributions is obtained. We show: The convolution of two Roumieu ultradistributions T, S ∈ D’{Mp} (Rn) exists if and only if (φ ∗ Š) T ∈ D’{Mp}L1(Rn) for every φ ∈ D {Mp} (Rn). We study boundary values of holomorphic functions defined in tube domains. New edge of the wedge theorems are obtained. The resultsare then applied to represent D’E’* as a quotient space of holomorphic functions.We also give representations of elements of D’E’* via the heat kernel method.Koristimo oznaku ∗ za distribuciono (Svarcovo), (Mp) (Berlingovo) i {Mp} (Roumieuovo) okruženje. Uvodimo i prouavamo nove (ultra)distribucione prostore, test funkcijske prostore D∗E i njihove duale D'∗E'*. Ovi prostori uopštavaju prostore D∗Lq , D'∗Lp , B'∗ i njihove težinske verzije. Konstrukcija naših novih (ultra)distribucionih prostora je zasnovana na analizi odgovarajuićh translaciono - invarijantnih Banahovih prostora (ultra)distribucija koje označavamo sa E. Ovi prostori imaju neprekidnu grupu translacija, koja je konvolucioni modul nad Beurlingovom algebrom L1ω, gde je težina ω povezana sa operatorima translacije prostora E. Banahov prostor E'∗ označava prostor L1ω˅ ∗ E'. Koristeći dobijene rezultata proučavamo konvoluciju ultradistribucija. Prostori konvolutora O'∗C (Rn) temperiranih ultradistribucija, analizirani su pomoću dualnosti test funkcijskih prostora O∗C (Rn), definisanih u ovoj tezi. Koristeći svojstva translaciono - invarijantnih Banahovih prostora temperiranih ultradistribucija, opet označenih sa E, dobijamo karakterizaciju konvolucije Romuieu-ovih ultradistribucija, preko integrabilnih ultradistribucija. Dokazujemo da: konvolucija dve Roumieu-ove ultradistribucija T, S ∈ D'{Mp} (Rn) postoji ako i samo ako (φ ∗ Sˇ)T ∈ D'{Mp} L1 (Rn) za svaki φ ∈ D{Mp}(Rn). Takođe, proučavamo granične vrednosti holomorfnih funkcija definisanih na tubama. Dokazane su nove teoreme ”otrog klina”. Rezultati se zatim koriste za prezentaciju D'E'∗ preko faktor prostora holomorfnih funkcija. Takođe, data je prezentacija elemente D'E'∗ koristeći heat kernel metode.
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Vasil'ev, Vladimir A. "Invertibility of a class of Toeplitz operators over the half plane." [S.l. : s.n.], 2007.
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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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Fredriksson, Henrik. "Wiener's lemma." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-27270.
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In this thesis we study Wiener’s lemma. The classical version of the lemma, whose realm is a Banach algebra, asserts that the pointwise inverse of a nonzero function with absolutely convergent Fourier expansion, also possesses an absolutely convergent Fourier expansion. The main purpose of this thesis is to investigate the validity inalgebras endowed with a quasi-norm or a p-norm.As a warmup, we prove the classical version of Wiener’s lemma using elemen-tary analysis. Furthermore, we establish results in Banach algebras concerning spectral theory, maximal ideals and multiplicative linear functionals and present a proof Wiener’s lemma using Banach algebra techniques. Let ν be a submultiplicative weight function satisfying the Gelfand-Raikov-Shilov condition. We show that if a nonzero function f has a ν-weighted absolutely convergent Fourier series in a p-normed algebra A. Then 1/f also has a ν-weightedabsolutely convergent Fourier series in A.
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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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Cowell, S. R. "Unitary Banach algebras." Thesis, Swansea University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636306.
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Chapter 1 defines the notion of a unitary Banach algebra, and gives various examples. The inheritance of the unitary property of quotients and subalgebras is investigated, the main result being that the class of unitary Banach algebras is exactly the class of quotients of discrete group algebras. One problem that is discussed is whether a unitary subalgebra needs to inherit the unit element. Chapter 2 gives several other characterisations of unitary Banach algebras among norm-unital Banach algebras, in particular by conditions on the numerical range. The topological properties of the unitary Banach algebra are also discussed. Chapter 3 deals with isometric isomorphisms of unitary Banach algebras. In particular it is shown that, for groups G1 and G2, and A a norm-unital Banach algebra with connected unitary group, or a unital C*-algebra, the existence of an isometric isomorphism from l1 (G1, A) onto ll (G2, A) implies that G1 and G2 are isomorphic. If A is commutative then these two results can be generalised to be case of locally compact abelian groups G1 and G2, and the Banach algebras L1(G1, A) and L1 (G2, A).
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Kaiser, Robert. "Polynomiale Kollokations-Quadraturverfahren für singuläre Integralgleichungen mit festen Singularitäten." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-229930.
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Viele Probleme der Riss- und Bruchmechanik sowie der mathematischen Physik lassen sich auf Lösungen von singulären Integralgleichungen über einem Intervall zurückführen. Diese Gleichungen setzen sich im Wesentlichen aus dem Cauchy'schen singulären Integraloperator und zusätzlichen Integraloperatoren mit festen Singularitäten in den jeweiligen Kernen zusammen. Zur numerischen Lösung solcher Gleichungen werden polynomiale Kollokations-Quadraturverfahren betrachet. Als Ansatzfunktionen und Kollokationspunkte werden dabei gewichtete Polynome und Tschebyscheff-Knoten gewählt. Die Gewichte sind so gewählt, dass diese das asymptotische Verhalten der Lösung in den Randpunkten widerspiegeln. Mit Hilfe von C*-Algebra Techniken, werden in dieser Arbeit notwendige und hinreichende Bedingungen für die Stabilität der Kollokations-Quadraturverfahren angegeben. Die theoretischen Resultate werden dabei durch numerische Berechnungen anhand des Problems der angerissenen Halbebene und des angerissenen Loches überprüft.
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Daws, Matthew David Peter. "Banach algebras of operators." Thesis, University of Leeds, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414151.
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Gourdeau, Frederic Marcel. "Amenability of Banach algebras." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305500.
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Heath, Matthew J. "Bounded derivations from Banach algebras." Thesis, University of Nottingham, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.519425.
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Feinstein, Joel Francis. "Derivations from Banach function algebras." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329058.
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Choi, Yemon. "Cohomology of commutative Banach algebras and l¹-semigroup algebras." Thesis, University of Newcastle Upon Tyne, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427291.
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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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Schick, G. J. "Spectrally bounded operators on Banach algebras." Thesis, Queen's University Belfast, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390862.
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Bland, William J. "Banach function algebras and their properties." Thesis, University of Nottingham, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364660.
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Oliver, Thomas. "Extensions of endomorphisms of Banach algebras." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432001.
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Pourabbas, Abdolrasoul. "The cohomology of some Banach algebras." Thesis, University of Newcastle Upon Tyne, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318540.
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Zsák, András. "Algebras of operators on Banach spaces." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621830.
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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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Kuo, Po Ling. "Algebras de Banach de funções continuas." [s.n.], 2003. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306891.
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Orientador : Jorge Tulio Mujica AscuiDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Mestrado
Mestre em Matemática
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Bertoloto, Fábio José. "Algebras de Banach de funções analiticas." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307335.
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Orientador: Jorge Tulio Mujica AscuiDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação
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Resumo: O principal objetivo deste trabalho é o estudo de certos espaços de Banach de funções analíticas no disco aberto unitário, conhecidos como espaços de Hardy. Um outro objetivo é o estudo das propriedades básicas de álgebras de Banach, com especial ênfase na álgebra do disco e na álgebra das funções analíticas e limitadas no disco aberto unitário
Abstract: The main objective of this work is the study of certain Banach spaces of analytic functions on the open unit disc, known as Hardy spaces. Another objective is the study of the basic properties of Banach algebras, with special emphasis in the disc algebra and the algebra of bounded analytic functions in the open unit disc
Mestrado
Matematica
Mestre em Matemática
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White, Jared. "Banach algebras on groups and semigroups." Thesis, Lancaster University, 2018. http://eprints.lancs.ac.uk/125490/.
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This thesis concerns the theory of Banach algebras, particularly those coming from abstract harmonic analysis. The focus for much of the thesis is the theory of the ideals of these algebras. In the final chapter we use semigroup algebras to solve an open probelm in the theory of C*-algebras. Throughout the thesis we are interested in the interplay between abstract algebra and analysis. Chapters 2, 4, and 5 are closely based upon the articles [88], [89], and [56], respectively. In Chapter 2 we study (algebraic) finite-generation of closed left ideals in Banach algebras. Let G be a locally compact group. We prove that the augmentation ideal in L 1 pGq is finitely-generated as a left ideal if and only if G is finite. We then investigate weighted versions of this result, as well as a version for semigroup algebras. Weighted measure algebras are also considered. We are motivated by a recent conjecture of Dales and Żelazko, which states that a unital Banach algebra in which every maximal left ideal is finitely-generated is necessarily finite-dimensional. We prove that this conjecture holds for many of the algebras considered. Finally, we use the theory that we have developed to construct some examples of commutative Banach algebras that relate to a theorem of Gleason. In Chapter 3 we turn our attention to topological finite-generation of closed left ideals in Banach algebras. We define a Banach algebra to be topologically left Noetherian if every closed left ideal is topologically finitely-generated, and we seek infinitedimensional examples of such algebras. We show that, given a compact group G, the group algebra L 1 pGq is topologically left Noetherian if and only if G is metrisable. For a Banach space E satisying a certain condition we show that the Banach algebra of approximable operators ApEq is topologically left Noetherian if and only if E 1 is separable, whereas it is topologically right Noetherian if and only if E is separable. We also define what it means for a dual Banach algebra to be weak*-topologically left Noetherian, and give examples which satisfy and fail this condition. Along the way, we give classifications of the weak*-closed left ideals in MpGq, for G a compact group, and in BpEq, for E a reflexive Banach space with AP. Chapter 4 looks at the Jacobson radical of the bidual of a Banach algebra. We prove that the bidual of a Beurling algebra on Z, considered as a Banach algebra with the first Arens product, can never be semisimple. We then show that rad p` 1 p‘8 i“1Zq 2 q contains nilpotent elements of every index. Each of these results settles a question of Dales and Lau. Finally we show that there exists a weight ω on Z such that the bidual of ` 1 pZ, ωq contains a radical element which is not nilpotent. In Chapter 5 we move away from the theory of ideals and consider a question about the notion of finiteness in C*-alegebras. We construct a unital pre-C*-algebra A0 which is stably finite, in the sense that every left invertible square matrix over A0 is right invertible, while the C*-completion of A0 contains a non-unitary isometry, and so it is infinite. This answers a question of Choi. The construction is based on semigroup algebras.
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Oberbroeckling, Lisa A. "Generalized inverses in certain Banach algebras /." view abstract or download file of text, 2002. http://wwwlib.umi.com/cr/uoregon/fullcit?p3055703.
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Thesis (Ph. D.)--University of Oregon, 2002.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 57-58). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p3055703.
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Moore, David. "Endomorphisms of commutative unital Banach algebras." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/39674/.
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This thesis is a collection of theorems which say something about the following question: if we know that a bounded operator on a commutative unital Banach algebra is a unital endomorphism, what can we say about its other properties? More specifically, the majority of results say something about how the spectrum of a commutative unital Banach algebra endomorphism is dependent upon the properties of the algebra on which it acts. The main result of the thesis (the subject of Chapter 3) reveals that primary ideals (that is, ideals with single point hulls) can sometimes be particularly important in questions of this type. The thesis also contains some contributions to the Fredholm theory for bounded operators on an arbitrary complex Banach space. The second major result of the thesis is in this direction, and concerns the relationship between the essential spectrum of a bounded operator on a Banach space and those of its restrictions and quotients - `to' and `by' - closed invariant subspaces.
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Bird, Alistair. "A study of James-Schreier spaces as Banach spaces and Banach algebras." Thesis, Lancaster University, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.551626.
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We define and study a new family of Banach spaces, the J ames-Schreier spaces, cre- ated by combining key properties in the definitions of two important classical Banach spaces, namely James' quasi-reflexive space and Schreier's space. We explore both the Banach space and Banach algebra theory of these spaces. The new spaces inherit aspects of both parent spaces: our main results are that the J ames-Schreier spaces each have a shrinking basis, do not embed in a Banach space with an unconditional basis, and each of their closed, infinite-dimensional subspaces contains a copy of Co. As Banach sequence algebras each James-Schreier space has a bounded approx- imate identity and is weakly amenable but not amenable, and the bidual and multiplier - algebra are isometrically isomorphic. We approach our study of Banach sequence algebras from the point of view of Schauder basis theory, in particular looking at those Banach sequence algebras for which the unit vectors form an unconditional or shrinking basis. We finally show that for each Banach space X with an unconditional basis we may construct a James-like Banach sequence algebra j(X) with a bounded approximate identity, and give a condition on the shift operators acting on X which implies that j(X) will contain a copy of X as a complemented ideal and hence not be amenable.
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Zhang, Yong. "Amenability and weak amenability of Banach algebras." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0004/NQ41635.pdf.
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Howey, Richard Andrew Jonathon. "Approximately multiplicative maps between some Banach algebras." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324859.
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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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Weigt, Martin. "Spectrum preserving linear mappings between Banach algebras." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53597.
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Thesis (MSc)--University of Stellenbosch, 2003.ENGLISH ABSTRACT: Let A and B be unital complex Banach algebras with identities 1 and I' respectively. A linear map T : A -+ B is invertibility preserving if Tx is invertible in B for every invertible x E A. We say that T is unital if Tl = I'. IfTx2 = (TX)2 for all x E A, we call T a Jordan homomorphism. We examine an unsolved problem posed by 1. Kaplansky: Let A and B be unital complex Banach algebras and T : A -+ B a unital invertibility preserving linear map. What conditions on A, Band T imply that T is a Jordan homomorphism? Partial motivation for this problem are the Gleason-Kahane-Zelazko Theorem (1968) and a result of Marcus and Purves (1959), these also being special instances of the problem. We will also look at other special cases answering Kaplansky's problem, the most important being the result stating that if A is a von Neumann algebra, B a semi-simple Banach algebra and T : A -+ B a unital bijective invertibility preserving linear map, then T is a Jordan homomorphism (B. Aupetit, 2000). For a unital complex Banach algebra A, we denote the spectrum of x E A by Sp (x, A). Let a(x, A) denote the union of Sp (x, A) and the bounded components of
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Skillicorn, Richard. "Discontinuous homomorphisms from Banach algebras of operators." Thesis, Lancaster University, 2016. http://eprints.lancs.ac.uk/79356/.
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The relationship between a Banach space X and its Banach algebra of bounded operators B(X) is rich and complex; this is especially so for non-classical Banach spaces. In this thesis we consider questions of the following form: does there exist a Banach space X such that B(X) has a particular (Banach algebra) property? If not, is there a quotient of B(X) with the property? The first of these is the uniqueness-of-norm problem for Calkin algebras: does there exist a Banach space whose Calkin algebra lacks a unique complete norm? We show that there does indeed exist such a space, answering a classical open question [101]. Secondly, we turn our attention to splittings of extensions of Banach algebras. Work of Bade, Dales and Lykova [12] inspired the problem of whether there exist a Banach space X and an extension of B(X) which splits algebraically but not strongly; this asks for a special type of discontinuous homomorphism from B(X). Using the categorical notion of a pullback we obtain, jointly with N. J. Laustsen [71], new general results about extensions and prove that such a space exists. The same space is used to answer our third question, which goes back to Helemskii, in the positive: is there a Banach space X such that B(X) has homological bidimension at least two? The proof uses techniques developed (with N. J. Laustsen [71]) during the solution to the second question. We use two main Banach spaces to answer our questions. One is due to Read [90], the other to Argyros and Motakis [8]; the former plays a much more prominent role. Together with Laustsen [72], we prove a major original result about Read’s space which allows for the new applications. The conclusion of the thesis examines a class of operators on Banach spaces which have previously received little attention; these are a weak analogue of inessential operators.
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Morley, Sam. "Regularity and extensions of Banach function algebras." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/43358/.
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In this thesis we investigate the properties of various Banach function algebras and uniform algebras. We are particularly interested in regularity of Banach function algebras and extensions of uniform algebras. The first chapter contains the background in normed algebras, Banach function algebras, and uniform algebras which will be required throughout the thesis. In the second chapter we investigate the classicalisation of certain compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Sets obtained in this manner are called Swiss cheese sets. We give a new topological proof of the Feinstein-Heath classicalisation theorem along with similar results. We conclude the chapter with an application of the classicalisation results. The results in this chapter are joint with H. Yang. In the third chapter we study Banach function algebras of functions satisfying a generalised notion of differentiability. These algebras were first investigated by Bland and Feinstein as a way to describe the completion of certain normed algebras of complex-differentiable functions. We prove a new version of chain rule in this setting, generalising a result of Chaobankoh, and use this chain rule to give a new proof of the quotient rule. We also investigate naturality and homomorphisms between these algebras. In the fourth chapter we continue the study of the notion of differentiability from the third chapter. We investigate a new notion of quasianalyticity in this setting and prove an analogue of the classical Denjoy-Carleman theorem. We describe those functions which satisfy a notion of analyticity, and give an application of these results. In the fifth chapter we investigate various methods for constructing extensions of uniform algebras. We study the structure of Cole extensions, introduced by Cole and later investigated by Dawson, relative to certain projections. We also discuss a larger class of extensions, which we call generalised Cole extensions, originally introduced by Cole and Feinstein. In the final chapter we investigate extensions of derivations from uniform algebras. We prove that there exists a non-trivial uniform algebra such that every derivation extends with the same norm to every generalised Cole extension of that algebra. A non-trivial, weakly amenable uniform algebra satisfies this property. We also investigate a sequence of extensions of a derivation from the disk algebra.
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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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Vasilyev, Vladimir. "Invertibility of a Class of Toeplitz Operators over the Half Plane." Doctoral thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200700157.
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This dissertation is concerned with invertibility and
one-sided invertibility of Toeplitz operators
over the half plane whose generating functions
admit homogenous discontinuities, and with
stability of their pseudo finite sections.
The invertibility criterium is given in terms
of invertibility of a family of one
dimensional Toeplitz operators with piecewise
continuous generating functions. The one-sided
invertibility criterium is given it terms of
constraints on the partial indices of certain
Toeplitz operator valued function.
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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