State Spaces of Operator Algebras (Paperback)

Erik M. Alfsen

ISBN 10: 1461266343 / ISBN 13: 9781461266341

Published by Springer-Verlag New York Inc., New York, 2012

About this Item

Paperback. The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781461266341

Bibliographic Details

• Title: State Spaces of Operator Algebras (Paperback)
• Publisher: Springer-Verlag New York Inc., New York
• Publication Date: 2012
• Language: English
• ISBN 10: 1461266343
• ISBN 13: 9781461266341
• Binding: Paperback
• Condition: new

About this title

Synopsis

Self-contained work, focusing on the theory of state spaces of C*- algebras and von Neumann algebras. Gives a new presentation of the theory of orientation of state spaces of C*-algebras that does not depend on Jordan algebras. Also presented is the theory of orientation of normal state spaces of von Neumann algebras, with complete proofs for the first time. Minimal prerequisites: knowledge from standard graduate courses in real and complex variables, measure theory, and functional analysis. Intended for specialists in operator algebras, as well as graduate students and mathematicians seeking an overview of the field.

Review

"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