Geometry of State Spaces of Operator Algebras

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

I: Jordan Algebras and Their State Spaces.- 1: JB-algebras.- 2: JBW-algebras.- 3: Structure of JBW-algebras.- 4: Representations of JB-algebras.- 5: State Spaces of Jordan Algebras.- 6: Dynamical Correspondences.- II: Convexity and Spectral Theory.- 7: General Compressions.- 8: Spectral Theory.- III: State Space Characterizations.- 9: Characterization of Jordan Algebra State Spaces.- 10: Characterization of Normal State Spaces of von Neumann Algebras.- 11: Characterization of C*-algebra State Spaces.

Erscheinungsjahr:	2012
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	488
Reihe:	Mathematics: Theory & Applications
Inhalt:	xiii 467 S.
ISBN-13:	9781461265757
ISBN-10:	1461265754
Sprache:	Englisch
Herstellernummer:	80097772
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Shultz, Frederic W. Alfsen, Erik M.
Auflage:	Softcover reprint of the original 1st ed. 2003
Hersteller:	Birkhuser Boston Birkhäuser Boston Mathematics: Theory & Applications
Maße:	235 x 155 x 27 mm
Von/Mit:	Frederic W. Shultz (u. a.)
Erscheinungsdatum:	23.10.2012
Gewicht:	0,733 kg

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