Advertisement

Geometry of State Spaces of Operator Algebras

  • Erik M. Alfsen
  • Frederic W. Shultz

Part of the Mathematics: Theory & Applications book series (MTA)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jordan Algebras and Their State Spaces

    1. Front Matter
      Pages 1-1
    2. Erik M. Alfsen, Frederic W. Shultz
      Pages 3-35
    3. Erik M. Alfsen, Frederic W. Shultz
      Pages 37-77
    4. Erik M. Alfsen, Frederic W. Shultz
      Pages 79-102
    5. Erik M. Alfsen, Frederic W. Shultz
      Pages 103-138
    6. Erik M. Alfsen, Frederic W. Shultz
      Pages 139-189
    7. Erik M. Alfsen, Frederic W. Shultz
      Pages 191-207
  3. Convexity and Spectral Theory

    1. Front Matter
      Pages 209-209
    2. Erik M. Alfsen, Frederic W. Shultz
      Pages 211-249
    3. Erik M. Alfsen, Frederic W. Shultz
      Pages 251-312
    4. Erik M. Alfsen, Frederic W. Shultz
      Pages 315-355
  4. State Space Characterizations

    1. Front Matter
      Pages 313-313
    2. Erik M. Alfsen, Frederic W. Shultz
      Pages 357-373
    3. Erik M. Alfsen, Frederic W. Shultz
      Pages 375-417
  5. Back Matter
    Pages 419-467

About this book

Introduction

In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non­ associative algebras generalize C*-algebras and von Neumann algebras re­ spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character­ ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.

Keywords

Algebra applications mathematics functional analysis knot theory manifolds mathematical physics operator algebra

Authors and affiliations

  • Erik M. Alfsen
    • 1
  • Frederic W. Shultz
    • 2
  1. 1.Mathematical InstituteUniversity of OsloOsloNorway
  2. 2.Department of MathematicsWellesley CollegeWellesleyUSA

Bibliographic information