**Contemporary Mathematics**

Volume: 365;
2004;
422 pp;
Softcover

MSC: Primary 01; 19; 22; 46; 58; 81;

Print ISBN: 978-0-8218-3402-2

Product Code: CONM/365

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-0-8218-7955-9
Product Code: CONM/365.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

# Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone

Share this page *Edited by *
*Robert S. Doran; Richard V. Kadison*

John von Neumann and Marshall Stone were two giants of Twentieth Century
mathematics. In honor of the 100th anniversary of their births, a mathematical
celebration was organized featuring developments in fields where both men were
major influences.

This volume contains articles from the AMS Special Session, Operator Algebras,
Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of
John von Neumann and Marshall H. Stone. Papers range from expository and
historical surveys to original research articles. All articles were carefully
refereed and cover a broad range of mathematical topics reflecting the
fundamental ideas of von Neumann and Stone.

Most contributions are expanded versions of the talks and were written
exclusively for this volume. Included, among others, are articles by George
W. Mackey, Nigel Higson, and Marc Rieffel. Also featured is a reprint of
P.R. Halmos's The Legend of John von Neumann.

The book is suitable for graduate students and researchers interested in
operator algebras and applications, including noncommutative geometry.

#### Readership

Graduate students and research mathematicians interested in operator algebras and applications, including noncommutative geometry.

# Table of Contents

## Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring John von Neumann and Marshall H. Stone

- Contents v6 free
- Preface vii8 free
- The Legend of John von Neumann 110 free
- Marshall H. Stone: Mathematician, Statesman, Advisor, and Friend 1524
- The Universal A-Dynamical System 2736
- On the Index of Equivariant Elliptic Operators 4150
- The Algebraization of Dynamics: Amenability, Nuclearity, Quasidiagonality, and Approximate Finite Dimensionality 5160
- Multipliers, C*-modules, and Algebraic Structure in Spaces of Hilbert Space Operators 8594
- Meromorphic Continuation of Zeta Functions Associated to Elliptic Operators 129138
- Non-commutative Conditional Expectations and their Applications 143152
- Outer Actions of a Discrete Amenable Group on Approximately Finite Dimensional Factors I: General Theory 181190
- §0. Introduction 182191
- §1. Preliminary and notations 185194
- §2. Modified Huebschmann Jones Ratcliffe exact sequence 187196
- §3. Outer Actions of a discrete group on a factor 220229
- §4. Model construction 228237
- §5. Non-triviality of the exact sequence: 1 → H1θ → Out(M) → Out┬,θ(M) → 1 231240
- §6. Concluding remark 234243

- On the Curvature of a Completely Positive Map 239248
- Applications of the Work of Stone and von Neumann to Wavelets 253262
- Addition of Spatial E0 -Semigroups 281290
- On Shifts of Minimal Index on the Hyperfinite II1 Factor 299308
- Compact Quantum Metric Spaces 315324
- A Selective History of the Stone-von Neumann Theorem 331340
- Decomposable Maps on Non-commutative Lp-spaces 355364
- A Survey of Hochschild Cohomology for von Neumann Algebras 383392
- From the Stone-von Neumann Theorem to the Equivariant Brauer Group and Beyond 401410