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A Course in Commutative Banach Algebras

A Course in Commutative Banach Algebras PDF Author: Eberhard Kaniuth
Publisher: Springer Science & Business Media
ISBN: 0387724761
Category : Mathematics
Languages : en
Pages : 362

Book Description
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.

A Course in Commutative Banach Algebras

A Course in Commutative Banach Algebras PDF Author: Eberhard Kaniuth
Publisher: Springer Science & Business Media
ISBN: 0387724761
Category : Mathematics
Languages : en
Pages : 362

Book Description
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.

General Theory of Banach Algebras

General Theory of Banach Algebras PDF Author: Charles Earl Rickart
Publisher: Krieger Publishing Company
ISBN:
Category : Algebraic fields
Languages : en
Pages : 416

Book Description


M-Ideals in Banach Spaces and Banach Algebras

M-Ideals in Banach Spaces and Banach Algebras PDF Author: Peter Harmand
Publisher: Springer
ISBN: 3540477535
Category : Mathematics
Languages : en
Pages : 390

Book Description
This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.

Introduction to Banach Algebras, Operators, and Harmonic Analysis

Introduction to Banach Algebras, Operators, and Harmonic Analysis PDF Author: H. Garth Dales
Publisher: Cambridge University Press
ISBN: 9780521535847
Category : Mathematics
Languages : en
Pages : 338

Book Description
Table of contents

A Short Course on Spectral Theory

A Short Course on Spectral Theory PDF Author: William Arveson
Publisher: Springer Science & Business Media
ISBN: 0387953000
Category : Mathematics
Languages : en
Pages : 140

Book Description
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

Cohomology in Banach Algebras

Cohomology in Banach Algebras PDF Author: Barry Edward Johnson
Publisher: American Mathematical Soc.
ISBN: 0821818279
Category : Mathematics
Languages : en
Pages : 96

Book Description
Let [Fraktur capital]A be a Banach algebra, [Fraktur capital]X a two-sided Banach [Fraktur capital] A-module, and define the cohomology groups [italic]H[italic superscript]n([Fraktur capital]A, [Fraktur capital]X) from the complex of bounded cochains in exact analogy to the classical (algebraic) case. This article gives an introduction to several aspects of the resulting theory.

Banach Algebras and Several Complex Variables

Banach Algebras and Several Complex Variables PDF Author: John Wermer
Publisher: Springer Science & Business Media
ISBN: 1475738781
Category : Mathematics
Languages : en
Pages : 169

Book Description
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.

Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935

Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 PDF Author:
Publisher:
ISBN:
Category : Securities
Languages : en
Pages : 264

Book Description


Introduction to Banach Spaces and Algebras

Introduction to Banach Spaces and Algebras PDF Author: Graham Allan
Publisher: Oxford University Press
ISBN: 0199206538
Category : Mathematics
Languages : en
Pages : 380

Book Description
The text begins by giving the basic theory of Banach spaces, in particular discussing dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and to operators on Hilbert spaces. --

Banach Algebras and Applications

Banach Algebras and Applications PDF Author: Mahmoud Filali
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110602415
Category : Mathematics
Languages : en
Pages : 264

Book Description
Banach algebras is a multilayered area in mathematics with many ramifications. With a diverse coverage of different schools working on the subject, this proceedings volume reflects recent achievements in areas such as Banach algebras over groups, abstract harmonic analysis, group actions, amenability, topological homology, Arens irregularity, C*-algebras and dynamical systems, operator theory, operator spaces, and locally compact quantum groups.