**Contemporary Mathematics**

Volume: 534;
2011;
168 pp;
Softcover

MSC: Primary 43; 46; 47; 81;

Print ISBN: 978-0-8218-4905-7

Product Code: CONM/534

List Price: $73.00

AMS Member Price: $58.40

MAA Member Price: $65.70

**Electronic ISBN: 978-0-8218-8213-9
Product Code: CONM/534.E**

List Price: $73.00

AMS Member Price: $58.40

MAA Member Price: $65.70

# Aspects of Operator Algebras and Applications

Share this page *Edited by *
*Pere Ara; Fernando Lledó; Francesc Perera*

This volume contains survey papers on the
theory of operator algebras based on lectures given at the
“Lluís Santaló” Summer School of the Real
Sociedad Matemática Española, held in July 2008 at the
Universidad Internacional Menéndez Pelayo, in Santander
(Spain).

Topics in this volume cover current fundamental aspects of the theory of
operator algebras, which have important applications such as:

- \(K\)-Theory, the Cuntz semigroup, and Classification for \(C^*\)-algebras
- Modular Theory for von Neumann algebras and applications to Quantum Field Theory
- Amenability, Hyperbolic Groups, and Operator Algebras.

The theory of operator algebras, introduced in the thirties by J. von Neumann and F. J. Murray, was developed in close relationship with fundamental aspects of functional analysis, ergodic theory, harmonic analysis, and quantum physics. More recently, this field has shown many other fruitful interrelations with several areas of mathematics and mathematical physics.

This book is published in cooperation with Real Sociedad Matemática Española (RSME)

#### Readership

Graduate students and research mathematicians interested in operator algebras, \(C^*\)-algebras, and \(K\)-theory.

# Table of Contents

## Aspects of Operator Algebras and Applications

- Contents v6 free
- Preface vii8 free
- K-Theory for Operator Algebras. Classification of C*-algebras 110 free
- Modular Theory by Example 7382
- 1. Introduction 7382
- 2. Modular Theory: definitions, results and first examples 7483
- 3. Modular objects for a crossed product 7988
- 4. Modular objects for the CAR-algebra 8291
- 5. Some classical applications of Modular Theory 8998
- 6. Appendix: Crossed products and the CAR-algebra 91100
- References 93102

- Modular Theory for the Von Neumann Algebras of Local Quantum Physics 97106
- The Symbiosis of C*- and W*-algebras 121130
- Appendix: Basic Definitions and Results for Operator Algebras 157166