**Graduate Studies in Mathematics**

Volume: 16;
1997;
676 pp;
Hardcover

MSC: Primary 46;
Secondary 47

Print ISBN: 978-0-8218-0820-7

Product Code: GSM/16

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-1-4704-2073-4
Product Code: GSM/16.E**

List Price: $89.00

Individual Member Price: $71.20

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# 00: Advanced Theory

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*Richard V. Kadison; John R. Ringrose*

This work and Fundamentals of the Theory of Operator Algebras.
Volume I, Elementary 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

#### Table of Contents

# Table of Contents

## 00: Advanced Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface ix10 free
- Contents of Volume I xiii14 free
- Chapter 6. Comparison Theory of Projection 39924 free
- Chapter 7. Normal States and Unitary Equivalence of von Neumann Algebras 45479
- Chapter 8. The Trace 504129
- Chapter 9. Algebra and Commutant 584209
- Chapter 10. Special Representation of C*-Algebras 711336
- Chapter 11. Tensor Products 800425
- Chapter 12. Approximation by Matrix Algebras 889514
- Chapter 13 Crossed Products 936561
- Chapter 14 Direct Integrals and Decompositions 998623
- Bibliography 1049674
- Index of Notation 1055680 free
- Index 1061686
- Back Cover 1700

#### Readership

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

#### Reviews

What is presented here is an exciting and careful account of some very substantial mathematics! … As with the first volume, this book has an outstanding collection of exercises (and groupings of exercises) … Although the material in this second volume is substantially more advanced than that in the first volume, the authors have maintained the same spirit of freshness of the presentation given there.

-- Mathematical Reviews

This book is extremely clear and well written and ideally suited for an introductory course on the subject or for a student who wishes to learn the fundamentals of the classical theory of operator algebras.

-- Zentralblatt MATH

This volume by one of the co-founders of the isomorphism theory of Bernoulli processes offers a comprehensive treatment of finite-state stationary processes, with special emphasis on their combinatorial and coding properties. It is of interest to advanced graduate students and researchers working in ergodic theory, probability and information and gives an excellent account of many different tools and constructions of measure-theoretic dynamics … There is a useful bibliography which allows the interested reader to trace the history of the ideas presented in the book.

-- Monatshefte für Mathematik