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An Invitation to von Neumann Algebras / by V.S. Sunder.

Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and K-Theory. There seems...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Sunder, V. S.
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1987.
Series:Universitext.
Subjects:
Mathematics.
Global analysis (Mathematics)
Table of Contents:
  • 0 Introduction
  • 0.1 Basic operator theory
  • 0.2 The predual L(H)*
  • 0.3 Three locally convex topologies on L(H)
  • 0.4 The double commutant theorem
  • 1 The Murray
  • von Neumann Classification of Factors
  • 1.1 The relation ... ̃ ... (rel M)
  • 1.2 Finite projections
  • 1.3 The dimension function
  • 2 The Tomita
  • Takesaki Theory
  • 2.1 Noncommutative integration
  • 2.2 The GNS construction
  • 2.3 The Tomita-Takesaki theorem (for states)
  • 2.4 Weights and generalized Hilbert algebras
  • 2.5 The KMS boundary condition
  • 2.6 The Radon-Nikodym theorem and conditional expectations
  • 3 The Connes Classification of Type III Factors
  • 3.1 The unitary cocycle theorem
  • 3.2 The Arveson spectrum of an action
  • 3.3 The Connes spectrum of an action
  • 3.4 Alternative descriptions of?(M)
  • 4 Crossed-Products
  • 4.1 Discrete crossed-products
  • 4.2 The modular operator for a discrete crossed-product
  • 4.3 Examples of factors
  • 4.4 Continuous crossed-products and Takesaki's duality theorem
  • 4.5 The structure of properly infinite von Neumann algebras
  • Appendix: Topological Groups
  • Notes.

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