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Geometry of State Spaces of Operator Algebras
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Geometry of State Spaces of Operator Algebras

Geometry of State Spaces of Operator Algebras

Erik Alfsen, Frederic W. Shultz

480 pages, parution le 09/04/2003

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

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