**Graduate Studies in Mathematics**

Volume: 21;
2000;
372 pp;
Hardcover

MSC: Primary 47;

Print ISBN: 978-0-8218-2065-0

Product Code: GSM/21

List Price: $60.00

AMS Member Price: $48.00

MAA member Price: $54.00

**Electronic ISBN: 978-1-4704-2076-5
Product Code: GSM/21.E**

List Price: $60.00

AMS Member Price: $48.00

MAA member Price: $54.00

# A Course in Operator Theory

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*John B. Conway*

Operator theory is a significant part of many important areas of modern
mathematics: functional analysis, differential equations, index theory,
representation theory, mathematical physics, and more. This text covers the
central themes of operator theory, presented with the excellent clarity and
style that readers have come to associate with Conway's writing.

Early chapters introduce and review material on C*-algebras, normal
operators, compact operators and non-normal operators. The topics include the
spectral theorem, the functional calculus and the Fredholm index. Also, some
deep connections between operator theory and analytic functions are presented.

Later chapters cover more advanced topics, such as representations of
C*-algebras, compact perturbations and von Neumann algebras. Major results,
such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and
the classification of von Neumann algebras, are covered, as is a treatment of
Fredholm theory. These advanced topics are at the heart of current research.

The last chapter gives an introduction to reflexive subspaces, i.e., subspaces
of operators that are determined by their invariant subspaces. These, along
with hyperreflexive spaces, are one of the more successful episodes in the
modern study of asymmetric algebras.

Professor Conway's authoritative treatment makes this a compelling and rigorous
course text, suitable for graduate students who have had a standard course in
functional analysis.

#### Readership

Graduate students and research mathematicians interested in operator theory.

#### Reviews & Endorsements

John B. Conway belongs to the best authors of basic textbooks … The present book continues this tradition of clear and elegant way of presentation. … this book can be highly recommended for students of operator theory as well as to experts in the field who will find many interesting ideas there.

-- Mathematica Bohemica

Conway's book adds a complementary volume of study for those just becoming acquainted with the field … shares … a style which is relaxed, yet concise … recommend it to anyone wishing to gain a better understanding of operator theory.

-- Bulletin of the London Mathematical Society

This is an excellent course in operator theory and operator algebras … leads the reader to deep new results and modern research topics … the author has done more than just write a good book—he has managed to reveal the unspeakable charm of the subject, which is indeed the ‘source of happiness’ for operator theorists.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## A Course in Operator Theory

- Cover Cover11 free
- Title page v6 free
- Copyright vi7 free
- Dedication vii8
- Contents ix10 free
- Preface xiii14 free
- Chapter 1. Introduction to C*-algebras 118 free
- Chapter 2. Normal operators 3754
- Chapter 3. Compact operators 7188
- Chapter 4. Some non-normal operators 105122
- Chapter 5. More on C*-algebras 181198
- Chapter 6. Compact perturbations 207224
- Chapter 7. Introduction to von Neumann algebras 241258
- Chapter 8. Reflexivity 319336
- Bibliography 355372
- Index 367384
- List of Symbols 371388
- Back Cover Back Cover1390