Geometry of State Spaces of Operator Algebras (Paperback, Softcover reprint of the original 1st ed. 2003)

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 standard graduate courses in real and complex variables, measure theory, and functional analysis * Excellent bibliography and index In the authors' previous book, State Spaces of Operator Algebras: Basic Theory, Orientations and C*-products (ISBN 0-8176-3890-3), 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

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Mathematics: Theory & Applications
Release date:	March 2013
First published:	2003
Authors:	Erik M. Alfsen • Frederic W. Shultz
Dimensions:	235 x 155 x 24mm (L x W x T)
Format:	Paperback
Pages:	467
Edition:	Softcover reprint of the original 1st ed. 2003
ISBN-13:	978-1-4612-6575-7
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	1-4612-6575-4
Barcode:	9781461265757

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