**Graduate Studies in Mathematics**

Volume: 15;
1997;
398 pp;
Hardcover

MSC: Primary 46;
Secondary 47

Print ISBN: 978-0-8218-0819-1

Product Code: GSM/15

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

**Electronic ISBN: 978-1-4704-2072-7
Product Code: GSM/15.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

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# Fundamentals of the Theory of Operator Algebras. Volume I: Elementary Theory

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*Richard V. Kadison; John R. Ringrose*

The return of a classic!

This work and Fundamentals of the Theory of Operator Algebras.
Volume II, Advanced Theory present an introduction to functional analysis and the
initial fundamentals of \(C^*\)- and von Neumann algebra theory in a form
suitable for both intermediate graduate courses and self-study. The authors
provide a clear account of the introductory portions of this important and
technically difficult subject. Major concepts are sometimes presented from
several points of view; the account is leisurely when brevity would compromise
clarity. An unusual feature in a text at this level is the extent to which it
is self-contained; for example, it introduces all the elementary functional
analysis needed. The emphasis is on teaching. Well supplied with
exercises, the text assumes only basic measure theory and topology. The book
presents the possibility for the design of numerous courses aimed at different
audiences.

Praise for both volumes …

“ … these two volumes represent a magnificent achievement.
They will be an essential item on every operator algebraist's bookshelves and
will surely become the primary source of instruction for research students in
von Neumann algebra theory.”

—Bulletin of the London Mathematical Society

“Volumes I and II were published in 1982 and 1983. Since
then they have quickly established themselves as The Textbooks in operator
algebra theory.”

—Bulletin of the American Mathematical
Society

“One of the splendid features of the original two
volumes is their large supply of exercises … which illustrate the
results of the text and expand its scope.”

—L'Enseignement mathématique

#### Readership

Graduate students, research mathematicians, educators, and mathematical physicists interested in functional analysis, operator algebras, and applications.

#### Reviews & Endorsements

Drawing on their rich experience, the authors have succeeded in presenting a very attractive and well-written book that conveys the flavor and the beauty of classical operator algebra theory and that should be ideally suited as a text for a graduate course on the subject.

-- Zentralblatt MATH

The authors have presented it [the material] in a fresh and attractive way which conveys the spirit and beauty of the subject … a beautiful book.

-- Mathematical Reviews

Most of Volume I is devoted to three chapters of preparatory material. In fact, these chapters form a general introduction to functional analysis which could hardly be bettered.

-- Bulletin of the London Mathematical Society

#### Table of Contents

# Table of Contents

## Fundamentals of the Theory of Operator Algebras. Volume I: Elementary Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Contents of Volume II xiii14 free
- Chapter 1. Linear Spaces 118 free
- Chapter 2. Basics of Hilbert Space and Linear Operators 7592
- Chapter 3. Banach Algebras 173190
- Chapter 4. Elementary C*-Algebra Theory 236253
- Chapter 5. Elementary von Neumann Algebra Theory 304321
- 5.1. The weak- and strong- operator topologies 304321
- 5.2. Spectral theory for bounded operators 309326
- 5.3. Two fundamental approximation theorems 325342
- 5.4. Irreducible algebras—an application 330347
- 5.5. Projection techniques and constructs 332349
- 5.6. Unbounded operators and abelian von Neumann algebras 340357
- 5.7. Exercises 370387

- Bibliography 384401
- Index of Notation 387404 free
- Index 391408