# banach algebra techniques in operator theory graduate texts in mathematics

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## Banach Algebra Techniques In Operator Theory

**Author :**Ronald G. Douglas

**ISBN :**9781461216568

**Genre :**Mathematics

**File Size :**67. 50 MB

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A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends with source notes which suggest additional reading along with comments on who proved what and when, followed by a large number of problems of varying difficulty. This new edition will appeal to a whole new generation of students seeking an introduction to this topic.

## Banach Algebra Techniques In The Theory Of Toeplitz Operators

**Author :**Ronald G. Douglas

**ISBN :**0821888641

**Genre :**Mathematics

**File Size :**54. 66 MB

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## A Short Course On Spectral Theory

**Author :**William Arveson

**ISBN :**9780387215181

**Genre :**Mathematics

**File Size :**27. 43 MB

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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.

## A Course In Commutative Banach Algebras

**Author :**Eberhard Kaniuth

**ISBN :**9780387724768

**Genre :**Mathematics

**File Size :**23. 4 MB

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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 Banach Spaces And Algebras

**Author :**Graham R. Allan

**ISBN :**9780199206537

**Genre :**Banach algebras

**File Size :**74. 54 MB

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A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

## An Introduction To Banach Space Theory

**Author :**Robert E. Megginson

**ISBN :**9781461206033

**Genre :**Mathematics

**File Size :**90. 66 MB

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Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

## A Course In Functional Analysis

**Author :**John B. Conway

**ISBN :**9781475738285

**Genre :**Mathematics

**File Size :**83. 79 MB

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Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

## The Elements Of Operator Theory

**Author :**Carlos S. Kubrusly

**ISBN :**9780817649982

**Genre :**Mathematics

**File Size :**30. 85 MB

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This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem. Included in this edition: more than 150 examples, with several interesting counterexamples that demonstrate the frontiers of important theorems, as many as 300 fully rigorous proofs, specially tailored to the presentation, 300 problems, many with hints, and an additional 20 pages of problems for the second edition. *This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers.

## Analysis Now

**Author :**Gert K. Pedersen

**ISBN :**9781461210078

**Genre :**Mathematics

**File Size :**75. 63 MB

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Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view.

## Functional Analysis

**Author :**V.S. Sunder

**ISBN :**3764358920

**Genre :**Mathematics

**File Size :**30. 26 MB

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In an elegant and concise fashion, this book presents the concepts of functional analysis required by students of mathematics and physics. It begins with the basics of normed linear spaces and quickly proceeds to concentrate on Hilbert spaces, specifically the spectral theorem for bounded as well as unbounded operators in separable Hilbert spaces. While the first two chapters are devoted to basic propositions concerning normed vector spaces and Hilbert spaces, the third chapter treats advanced topics which are perhaps not standard in a first course on functional analysis. It begins with the Gelfand theory of commutative Banach algebras, and proceeds to the Gelfand-Naimark theorem on commutative C*-algebras. A discussion of representations of C*-algebras follows, and the final section of this chapter is devoted to the Hahn-Hellinger classification of separable representations of commutative C*-algebras. After this detour into operator algebras, the fourth chapter reverts to more standard operator theory in Hilbert space, dwelling on topics such as the spectral theorem for normal operators, the polar decomposition theorem, and the Fredholm theory for compact operators. A brief introduction to the theory of unbounded operators on Hilbert space is given in the fifth and final chapter. There is a voluminous appendix whose purpose is to fill in possible gaps in the reader's background in various areas such as linear algebra, topology, set theory and measure theory. The book is interspersed with many exercises, and hints are provided for the solutions to the more challenging of these.