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An invitation to von Neumann algebras

By: Material type: TextSeries: UniversitextPublication details: New York : Springer-Verlag, c1987.Description: xiv, 171 p. : ill. ; 24 cmISBN:
  • 0387963561 (pbk.) :
  • 9780387963563
Subject(s): DDC classification:
  • 512.55 19 SUN/I
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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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
General Books Central Library, Sikkim University General Book Section 512.55 SUN/I (Browse shelf(Opens below)) Available 053131
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Includes index.

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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