Author | Sunder, V. S. author |
---|---|
Title | An Invitation to von Neumann Algebras [electronic resource] / by V. S. Sunder |
Imprint | New York, NY : Springer New York, 1987 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8669-8 |
Descript | XIV, 172 p. online resource |
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 โ von Neumann Classification of Factors -- 1.1 The relationโฆ ̃โฆ (rel M) -- 1.2 Finite projections -- 1.3 The dimension function -- 2 The Tomita โ 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 Takesakiโs duality theorem -- 4.5 The structure of properly infinite von Neumann algebras -- Appendix: Topological Groups -- Notes