Geometry of State Spaces of Operator Algebras

Erik Alfsen, Frederic W. Shultz

480 pages, parution le 09/04/2003

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Résumé

This monograph presents a complete and self-contained solution to the long-standing problem of giving a geometric description of state spaces of C*-algebras and von Neumann algebras, and of their Jordan algebraic analogs (JB-algebras and JBW-algebras).
The material, which previously has appeared only in research papers and required substantial prerequisites for a reader's understanding, is made accessible here to a broad mathematical audience.

Key features include:

The properties used to describe state spaces are primarily of a geometric nature, but many can also be interpreted in terms of physics. There are numerous remarks discussing these connections A quick introduction to Jordan algebras is given; no previous knowledge is assumed and all necessary background on the subject is given
A discussion of dynamical correspondences, which tie together Lie and Jordan structures, and relate the observables and the generators of time evolution in physics
The connection with Connes' notions of orientation and homogeneity in cones is explained Chapters conclude with notes placing the material in historical context
Prerequisites are a standard graduate courses in real and complex variables, measure theory, and functional analysis
Excellent bibliography and index

In the authors previous book, State Space of Operator Algebras: Basic Theory, Orientations and C*-products, the role of orientations was examined and all the prerequisites on C*-algebras and von Neumann algebras, needed for this work, were provided in detail. These requisites, as well as all relevant definitions and results with reference back to State Spaces, are summarized in an appendix, further emphasizing the self-contained nature of this work.

Geometry of State Spaces of Operator Algebras is intended for specialists in operator algebras, as well as graduate students and mathematicians in other areas.

Contents

Jordan Algebras and Their State Spaces

JB-Algebras
JBW-Algebras
Structure of JBW-Algebras
Representations of JB-Algebras
State Spaces of Jordan Algebras
Dynamical Correspondences

Convexity and Spectral Theory

General Compressions
Spectral Theory

State Space Characterizations

Characterization of Jordan Algebra State Spaces
Characterization of Normal State Spaces of von Neumann Algebras
Characterization of C*-Algebra State Spaces

Appendix
Bibliography
Index

L'auteur - Erik Alfsen

University of Oslo

L'auteur - Frederic W. Shultz

Frederic W. Shultz, Wellesley College

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Erik Alfsen, Frederic W. Shultz
Parution	09/04/2003
Nb. de pages	480
Format	16 x 24
Couverture	Relié
Poids	850g
Intérieur	Noir et Blanc
EAN13	9780817643195
ISBN13	978-0-8176-4319-5