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An invitation to von Neumann algebras

Author: V S Sunder
Publisher: New York : Springer, 1987
Series: Universitext
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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Document Type: Book
All Authors / Contributors: V S Sunder
ISBN: 0387963561 9780387963563 3540963561 9783540963561
OCLC Number: 471900958
Description: xiv, 171 s.
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.
Series Title: Universitext
Responsibility: V.S. Sunder
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