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State Spaces of Operator Algebras : Basic Theory, Orientations, and C*-Products - E.M. Alfsen

State Spaces of Operator Algebras

Basic Theory, Orientations, and C*-Products

Hardcover Published: 27th April 2001
ISBN: 9780817638900
Number Of Pages: 350

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This self-contained work, focusing on the theory of state spaces of C*-algebras and von Neumann algebras, explains how the oriented state space geometrically determines the algebra. The theory of orientation of C*-algebra state spaces is presented with a new approach that does not depend on Jordan algebras, and the theory of orientation of normal state spaces of von Neumann algebras is presented with complete proofs for the first time. The theory of operator algebras was initially motivated by applications to physics, but has recently found unexpected new applications to fields of pure mathematics as diverse as foliations and knot theory. Key features include: * first and only work devoted to state spaces of operator algebras--contains much material not available in existing books * prerequisites are standard graduate courses in real and complex variables, measure theory, and functional analysis * complete proofs of basic results on operator algebras presented so that no previous knowledge in the field is needed * detailed introduction develops basic tools used throughout the text * numerous chapter remarks on advanced topics of independent interest with references to the literature, or discussion of applications to physics "State Spaces of Operator Algebras" is intended for specialists in operator algebras, as well as graduate students and mathematicians seeking an overview of the field. The introduction to C*-algebras and von Neumann algebras may also be of interest in it own right for those wanting a quick introduction to basic concepts in those fields.

Industry Reviews

"This excellent book was born out of the authors' successful attempts to answer questions [like] 'When is a compact convex set the state space of a C*-algebra?' . . . I would regard the book as essential reading for any graduate student working in C*-algebras and related areas, particularly those with an interest in geometry."

--Zentralblatt Math

"A useful introduction to an elegant aspect of the theory of operator algebras which has close links to mathematical physics, as well as being of interest in its own right."

--Mathematical Reviews

"This self-contained work, focusing on the theory of state spaces of C*-algebras and von Neumann algebras, explains how the oriented state space geometrically determines the algebra...The theory of operator algebras was initially motivated by applications to physics, but has recently found unexpected new applications to fields of pure mathematics as diverse as foliations and knot theory." ---Analele Stiintifice ale Universitatii, al. I. Cuza din Iasi

Preface
Introduction
Elementary Theory of C*-Algebras and von Neumann Algebras
Ideals, Faces and Compressions
The Normal State of Space of B(H)
States, Representations, and Orientations of C*-Algebras
Symmetries and Rotations in von Neumann Algebras
Orientations and von Neumann Algebras
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780817638900
ISBN-10: 0817638903
Series: Mathematics: Theory & Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 350
Published: 27th April 2001
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 2.24
Weight (kg): 0.69

Earn 294 Qantas Points
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