**Contemporary Mathematics**

Volume: 671;
2016;
267 pp;
Softcover

MSC: Primary 46; 19; 22;

**Print ISBN: 978-1-4704-1948-6
Product Code: CONM/671**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

**Electronic ISBN: 978-1-4704-3500-4
Product Code: CONM/671.E**

List Price: $108.00

AMS Member Price: $86.40

MAA Member Price: $97.20

# Operator Algebras and Their Applications: A Tribute to Richard V. Kadison

Share this page *Edited by *
*Robert S. Doran; Efton Park*

This volume contains the proceedings of the
AMS Special Session Operator Algebras and Their Applications: A
Tribute to Richard V. Kadison, held from January 10–11,
2015, in San Antonio, Texas.

Richard V. Kadison has been a towering figure in the study of
operator algebras for more than 65 years. His research and leadership
in the field have been fundamental in the development of the subject,
and his influence continues to be felt through his work and the work of
his many students, collaborators, and mentees.

Among the topics addressed in this volume are the Kadison-Kaplanksy
conjecture, classification of \(C^*\)-algebras, connections between
operator spaces and parabolic induction, spectral flow, \(C^*\)-algebra
actions, von Neumann algebras, and applications to mathematical
physics.

#### Readership

Graduate students and research mathematicians interested in Banach algebras and operator algebras.

# Table of Contents

## Operator Algebras and Their Applications: A Tribute to Richard V. Kadison

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Exactness and the Kadison-Kaplansky conjecture 114
- 1. Introduction 114
- 2. Exact groups and crossed products 316
- 3. Some properties of groups, spaces, and actions 518
- 4. Expanders 922
- 5. Gromov monster groups 1326
- 6. The Baum-Connes conjecture with coefficients 1629
- 7. Counterexamples to the Baum-Connes conjecture 1831
- 8. Reformulating the conjecture: exotic crossed products 2235
- 9. The counterexamples and the reformulated conjecture 2437
- 10. The Kadison-Kaplansky conjecture for ℓ¹(𝐺) 2841
- 11. Concluding remarks 2942
- References 3043

- Generalization of 𝐶*-algebra methods via real positivity for operator and Banach algebras 3548
- 1. Introduction 3548
- 2. Richard Kadison and the beginnings of positivity 3750
- 3. Real completely positive maps and projections 4154
- 4. More notation, and existence of ‘positive’ approximate identities 4558
- 5. Order theory in the unit ball 4962
- 6. Positivity and roots in Banach algebras 5164
- 7. Structure of ideals and HSA’s 5972
- References 6477

- Higher weak derivatives and reflexive algebras of operators 6982
- Parabolic induction, categories of representations and operator spaces 8598
- Spectral multiplicity and odd K-theory-II 109122
- On the classification of simple amenable C*-algebras with finite decomposition rank 117130
- Topology of natural numbers and entropy of arithmetic functions 127140
- 1. Introduction and definitions 127140
- 2. Constructions and examples of anqies 130143
- 3. Anqie entropy of arithmetic functions 132145
- 4. Anqie independence and semi-continuity of anqie entropy 135148
- 5. Invariant means on \N and GNS constructions 138151
- 6. Arithmetics and topologies 141154
- References 143156

- Properness conditions for actions and coactions 145158
- Reflexivity of Murray-von Neumann algebras 175188
- Hochschild cohomology for tensor products of factors 185198
- On the optimal paving over MASAs in von Neumann algebras 199212
- Matricial bridges for “Matrix algebras converge to the sphere” 209222
- 1. Introduction 209222
- 2. The first basic class of examples 210223
- 3. The second basic class of examples 213226
- 4. Bridges with conditional expectations 214227
- 5. The corresponding matricial bridges 219232
- 6. The application to the first class of basic examples 223236
- 7. The application to the second class of basic examples 227240
- 8. Treks 231244
- References 232245

- Structure and applications of real 𝐶*-algebras 235248
- Separable states, maximally entangled states, and positive maps 259272
- Back Cover Back Cover1282