Aspects of operator algebras and applications : UIMP-RSME Luís A. Santaló Summer School, Universidad Internacional Menéndez Pelayo, Santander, Spain, July 21-25, 2008

Contents.
Preface.
K-Theory For Operator Algebras. Classification Of C*-Algebras.
1. Introduction.
2. The Cuntz Semigroup: Definitions, Historical Origin And Technical Devices.
3. Hilbert C*-Modules. Kasparov'S Theorem.
4. The Category Cu.
5. Classification Of C*-Algebras.
References.
Modular Theory By Example.
1. Introduction.
2. Modular Theory: Definitions, Results And First Examples.
3. Modular Objects For A Crossed Product.
4. Modular Objects For The Car-Algebra.
5. Some Classical Applications Of Modular Theory.
6. Appendix: Crossed Products And The Car-Algebra.
References.
Modular Theory For The Von Neumann Algebras Of Local Quantum Physics.
1. Introduction.
2. Free Quantum Fields And Local Quantum Theories.
3. Bisognano-Wichmann Relations..
4. Modular Covariance And Modular Localization..
References.
The Symbiosis Of C*- And W*-Algebras.
Appendix: Basic Definitions And Results For Operator Algebras.
1. Introduction.
2. C*-Algebras.
3. Von Neumann Algebras.
References.