**Fields Institute Monographs**

Volume: 6;
1996;
309 pp;
Hardcover

MSC: Primary 46;
Secondary 16; 41; 47

Print ISBN: 978-0-8218-0599-2

Product Code: FIM/6

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-1-4704-3133-4
Product Code: FIM/6.E**

List Price: $75.00

Individual Member Price: $60.00

# C*-Algebras by Example

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*Kenneth R. Davidson*

A co-publication of the AMS and Fields Institute

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.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students, research mathematicians and physicists interested in functional analysis, C*-algebras, and operator theory.

#### Reviews & Endorsements

The book … occupies a special place among numerous textbooks and monographs as in the subject chosen by the author so also in the method of presentation of the material … Each chapter contains numerous interesting exercises … can be recommended as a good introduction in the theory of \(C^*\)-theory for all who are not yet under the charm of this remarkable theory as well as for specialists in the field as a collection of useful and carefully selected tools and methods … useful for numerous lectures as a textbook for special courses with different aspects of \(C^*\)-algebras.

-- Zentralblatt MATH

Altogether, a very commendable introduction and collection.

-- Monatshefte für Mathematik

One can assign parts of Davidson's book to good students learning the subject and expect good results … the details persist even when the going gets tough … this is the only book I know in which one can go through the BDF classification of essentially normal operators and follow, point by point, to the end.

-- Bulletin of the AMS

The writing is exceptionally clear and easy to follow … an outstanding book that should be on every operator algebraist's bookshelf.

-- Mathematical Reviews

Very useful as a compendium of the common classes of nuclear \(C^*\)-algebras, to which it provides an excellent introduction. A good collection of exercises is provided.

-- Bulletin of the London Mathematical Society

A great book for a beginning grad course!

-- Palle Jorgensen

#### Table of Contents

# Table of Contents

## C*-Algebras by Example

- Cover Cover11
- Title page v6
- Dedication vii8
- Contents ix10
- Preface xiii14
- Chapter I. The basics of C*-algebras 116
- Chapter II. Normal operators and abelian C*-algebras 4661
- Chapter III. Approximately finite dimensional (AF) C*-algebras 7489
- Chapter IV. 𝐾-theory for AF C*-algebras 97112
- Chapter V. C*-algebras of isometries 132147
- Chapter VI. Irrational rotation algebras 166181
- Chapter VII. Group C*-algebras 182197
- Chapter VIII. Discrete crossed products 216231
- Chapter IX. Brown-Douglas-Fillmore theory 252267
- References 303318
- Index 307322
- Back Cover Back Cover1325