| Geometry of State Spaces of Operator Algebras 2003 Edition Contributor(s): Alfsen, Erik M. (Author), Shultz, Frederic W. (Author) |
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ISBN: 0817643192 ISBN-13: 9780817643195 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: December 2002 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Science | Physics - Quantum Theory - Mathematics | Algebra - General - Mathematics | Applied |
| Dewey: 512 |
| LCCN: 2002034257 |
| Series: Mathematics: Theory & Applications |
| Physical Information: 1.06" H x 6.38" W x 9.56" (1.89 lbs) 467 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |