An invitation to von Neumann algebras
Material type: TextSeries: UniversitextPublication details: New York : Springer-Verlag, c1987Description: xiv, 171 p. : ill. ; 24 cmISBN: 0387963561 (pbk.) :; 9780387963563Subject(s): Von Neumann algebras | -- VonNeumann-AlgebraDDC classification: 512.55Item type | Current library | Call number | Status | Date due | Barcode | Item holds |
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General Books | Central Library, Sikkim University General Book Section | 512.55 SUN/I (Browse shelf(Opens below)) | Available | 053131 |
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512.55 HIL/C A Course in Homological Algebra/ | 512.55 ROB/R Ergodic theory and semisimple groups/ | 512.55 SAT/L Lie groups and algebras with applications to physics, geometry, and mechanics/ | 512.55 SUN/I An invitation to von Neumann algebras | 512.55 THO/E Emergence of the theory of lie groups: an essay in the history of mathematics, 1869-1926/ | 512.55 VAR/L Lie groups, Lie algebras, and their representations/ | 512.55 VIN/L Linear representatives of groups/ |
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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