**Fields Institute Monographs**

Volume: 13;
2000;
323 pp;
Hardcover

MSC: Primary 46;

Print ISBN: 978-0-8218-0821-4

Product Code: FIM/13

List Price: $84.00

Individual Member Price: $67.20

**Electronic ISBN: 978-1-4704-3140-2
Product Code: FIM/13.E**

List Price: $84.00

Individual Member Price: $67.20

# Lectures on Operator Theory

Share this page *Edited by *
*B. V. Rajarama Bhat; George A. Elliott; Peter A. Fillmore*

A co-publication of the AMS and Fields Institute

This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of \(C^*\)-algebras and von Neumann algebras, together with recent work on the classification of \(C^*\)-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

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

#### Readership

Graduate students and research mathematicians interested in operator theory.

#### Reviews & Endorsements

Contains … a nice illustration of Elliott's classification techniques for inductive limits … richly illustrated article … on paths on Coxeter diagrams and sub-factors … particularly welcome … Overall this is a very nicely and surprisingly uniformly written book which is of interest both for the novice and the expert in operator algebras … It may be hoped that the book will inspire some young researcher to new invention.

-- CMS Notes

#### Table of Contents

# Table of Contents

## Lectures on Operator Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface xi12
- Part 1. C*-algebras 114
- C*-algebras: Definitions and examples 316
- C*-algebras: Constructions 922
- Positivity in C*-algebras 1730
- K-theory I 2538
- Tensor products of C*-algebras 3346
- Crossed products I 4356
- Crossed products II: Examples 4962
- Free products 5568
- K-theory II: Roots in topology and index theory 6376
- C*-algebraic K-theory made concrete, or trick or treat with 2×2 matrix algebras 7184
- Dilation theory 7790
- C*-algebras and mathematical physics 87100
- C*-algebras and several complex variables 91104
- Part 2. Von Neumann algebras 99112
- Basic structure of von Neumann algebras 101114
- von Neumann algebras (Type 𝐼𝐼₁ factors) 109122
- The equivalence between injectivity and hyperfiniteness, part I 115128
- The equivalence between injectivity and hyperfiniteness, part II 125138
- On the Jones index 135148
- Introductory topics on subfactors 141154
- The Tomita-Takesaki theory explained 151164
- Free products of von Neumann algebras 157170
- Semigroups of endomorphisms of ℬ(ℋ) 163176
- Part 3. Classification of C*-algebras 173186
- AF-algebras and Bratteli diagrams 175188
- Classification of amenable C*-algebras I 181194
- Classification of amenable C*-algebras II 187200
- Simple AI-algebras and the range of the invariant 193206
- Classification of simple purely infinite C*-algebras I 199212
- Part 4. Hereditary subalgebras of certain simple non real rank zero C*-algebras 207220
- Introduction 209222
- The isomorphism theorem 213226
- The range of the invariant 231244
- Bibliography 241254
- Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors 243256
- The Kauffman-Lins recoupling theory 245258
- Graphs and connections 253266
- An extension of the recoupling model 265278
- Relations to minimal models and subfactors 297310
- Bibliography 323336
- Back Cover Back Cover1337