| State Spaces of Operator Algebras: Basic Theory, Orientations, and C*-Products 2001 Edition Contributor(s): Alfsen, Erik M. (Author), Shultz, Frederik W. (Author) |
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ISBN: 0817638903 ISBN-13: 9780817638900 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: April 2001 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Functional Analysis - Mathematics | Applied |
| Dewey: 512.55 |
| LCCN: 2001025873 |
| Series: Mathematics: Theory & Applications |
| Physical Information: 0.88" H x 6.14" W x 9.21" (1.53 lbs) 350 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |