Noncommutative Dynamics and E-Semigroups / Edition 1

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This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. This monograph will be of interest to graduate students and research mathematicians.

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Editorial Reviews

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From the reviews:

"This book serves as a good introduction to the currently very active field of E0-semigroups. … This reviewer thinks that this is a timely publication in an area that has advanced rapidly in recent years … . the reviewer is happy to recommend this book." (Masamichi Takesaki, SIAM Review, Vol. 46 (4), 2004)

"The book is suitable for researchers and students who have had a first course in functional analysis … . For traditional researchers in operator algebras the book should be of interest because it looks at problems in a new way … . As someone who has been studying E0-semigroups for just shy of twenty years I am extremely pleased with the appearance of this valuable book, which I virtually carry with me." (Robert T. Powers, Mathematical Reviews, 2004 g)

"The author of this book is one of the great names in functional analysis … . The book has clearly been written with the goal of teaching the subject; the exposition is crisp, clear, and will be accessible to graduate students. … It is superbly written … . In addition to being the essential reference for those working on E0-semigroups, this magnificent book will be useful and inspirational to a wide range of mathematicians and mathematical physicists." (D. P. Blecher, Proceedings of the Edinburgh Mathematical Society, Vol. 49, 2006)

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Product Details

  • ISBN-13: 9781441918031
  • Publisher: Springer New York
  • Publication date: 12/14/2011
  • Series: Springer Monographs in Mathematics Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2003
  • Edition number: 1
  • Pages: 434
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.91 (d)

Table of Contents

• Dynamical Origins
• Part 1: Index and Perturbation Theory
• E-semigroups
• Continuous Tensor Products
• Spectral C*-algebras
• Part 2: Classification: Type I Cases
• Path Spaces
• Decomposable Product Systems
• Part 3: Noncommutative Laplacians
• CP-semigroups
• C*-Generators and Dilation Theory
• Index Theory for CP-Semigroups
• Bounded Generators
• Part 4: Causality and Dynamics
• Pure Perturbations of CAR/CCR Flows
• Interaction Theory
• Part 5: Type III Examples
• Powers' Examples
• Tsirelson-Vershik Product Systems
• Bibliography
• Index
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