A Course In Commutative Banach Algebras

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A Course In Commutative Banach Algebras

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Author : Eberhard Kaniuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-16

A Course In Commutative Banach Algebras written by Eberhard Kaniuth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-16 with Mathematics categories.

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.

Introduction To Tensor Products Of Banach Spaces

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Author : Raymond A. Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-15

Introduction To Tensor Products Of Banach Spaces written by Raymond A. Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-15 with Mathematics categories.

This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.

C Algebras And Operator Theory

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Author : Gerald J. Murphy
language : en
Publisher: Academic Press
Release Date : 2014-06-28

C Algebras And Operator Theory written by Gerald J. Murphy and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Banach Algebra Techniques In The Theory Of Toeplitz Operators

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Author : Ronald G. Douglas
language : en
Publisher: American Mathematical Soc.
Release Date : 1973

Banach Algebra Techniques In The Theory Of Toeplitz Operators written by Ronald G. Douglas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.

These notes are a corrected version of the lecture notes which were distributed to participants at a regional conference held at the University of Georgia on June 12-16, 1972. The theme of the lectures was the use of techniques drawn from the theory of Banach algebras to study Toeplitz operators. An attempt was made at unifying diverse results, and point of view and direction were stressed rather than completeness. In particular, many recent results and problems were discussed.

C Algebras By Example

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Author : Kenneth R. Davidson
language : en
Publisher: American Mathematical Society, Fields Institute
Release Date : 2023-10-04

C Algebras By Example written by Kenneth R. Davidson and has been published by American Mathematical Society, Fields Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-04 with Mathematics categories.

The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce–Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994–1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology. The variety of examples offered in this text expose the student to many of these connections. Graduate students with a solid course in functional analysis should be able to read this book. This should prepare them to read much of the current literature. This book is reasonably self-contained, and the author has provided results from other areas when necessary.

A Short Course On Spectral Theory

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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-09

A Short Course On Spectral Theory written by William Arveson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-09 with Mathematics categories.

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.

Banach Algebras And The General Theory Of Algebras Volume 1 Algebras And Banach Algebras

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Author : Theodore W. Palmer
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-25

Banach Algebras And The General Theory Of Algebras Volume 1 Algebras And Banach Algebras written by Theodore W. Palmer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-25 with Mathematics categories.

This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.

Operator Algebras

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Author : Bruce Blackadar
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-09

Operator Algebras written by Bruce Blackadar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-09 with Mathematics categories.

This volume attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of thesubject,howdoesthisvolumemakeasigni?cantadditiontotheliterature, and how does it di?er from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the ?rst paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume. I have tried to cover all of the main aspects of “standard” or “clas- cal” operator algebra theory; the goal has been to be, well, encyclopedic. Of course, in a subject as vast as this one, authors must make highly subjective judgments as to what to include and what to omit, as well as what level of detail to include, and I have been guided as much by my own interests and prejudices as by the needs of the authors of the more specialized volumes.

Banach Algebras And Their Applications

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Author : Anthony To-Ming Lau
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Banach Algebras And Their Applications written by Anthony To-Ming Lau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

Amenable Banach Algebras

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Author : Volker Runde
language : en
Publisher: Springer Nature
Release Date : 2020-03-03

Amenable Banach Algebras written by Volker Runde and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-03 with Mathematics categories.

This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.