Geometry of State Spaces of Operator Algebras / Edition 1

Geometry of State Spaces of Operator Algebras / Edition 1

by Erik M. Alfsen, Frederic W. Shultz
     
 

ISBN-10: 0817643192

ISBN-13: 9780817643195

Pub. Date: 12/13/2002

Publisher: Birkhauser Verlag

This book provides 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). This material, which has previously only appeared in research papers based on substantial prerequisites, is made

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Overview

This book provides 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). This material, which has previously only appeared in research papers based on substantial prerequisites, is made accessible to a broad mathematical audience.

The necessary prerequisites on C*-algebras and von Neumann algebras are summarized in an appendix, which contains all relevant definitions and results. All necessary background on Jordan algebras is given in the present book, and the first part of the book may be of independent interest for those wanting a quick introduction to Jordan algebras. This work will be of interest to researchers and students in operator algebras.

Product Details

ISBN-13:
9780817643195
Publisher:
Birkhauser Verlag
Publication date:
12/13/2002
Series:
Mathematics: Theory & Applications Series
Edition description:
2003
Pages:
467
Product dimensions:
6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Preface
Pt. IJordan Algebras and Their State Spaces1
Ch. 1JB-algebras3
Ch. 2JBW-algebras37
Ch. 3Structure of JBW-algebras79
Ch. 4Representations of JB-algebras103
Ch. 5State Spaces of Jordan Algebras139
Ch. 6Dynamical Correspondences191
Pt. IIConvexity and Spectral Theory209
Ch. 7General Compressions211
Ch. 8Spectral Theory251
Pt. IIIState Space Characterizations313
Ch. 9Characterization of Jordan Algebra State Spaces315
Ch. 10Characterization of Normal State Spaces of von Neumann Algebras357
Ch. 11Characterization of C[superscript *]-algebra State Spaces375
Appendix419
Bibliography451
Index459

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