Contents Introduction 1 Chapter I. Noncommutative Integration 3 Section 1. Left Hubert algebras 4 Section 2. Weights and Representations 12 Section 3. Left Hubert algebras and weights 14 Section 4. Weights and modular automorphism groups 16 Section 5. The centralizer of a weight 19 Section 6. Connes' theorem of Radon-Nikodym type 22 Section 7. Standard form of a von Neumann algebra 29 Chapter II. General Theory of Crossed Products and Duality 33 Section 1. Crossed products 34 Section 2. Duality for crossed products 37 Section 3. Arveson-Connes spectral theory 40 Section 4. Construction of covariant Systems 45 Section 5. Comparison of cocycles 50 Section 6. Galois correspondence. Abelian case 54 Section 7. Galois correspondence. Noncommutative case 57 Chapter III. Structure of Factors of Type III 59 Section 1. Crossed product decomposition of von Neumann algebras of type III 59 Section 2. Factors of type ÐÉ ë , 0 ë 1 65 Section 3. Factors of type III0 67 Section 4. Factors associated with ergodic transformation groups 70 Section 5. Flow of weights 73 Chapter IV. Connes' Theory of Injective Factors and Automorphisms 77 Section 1. Centralizing sequences 77 Section 2. Noncommutative F^lner's condition 82 Section 3. Characterizations of approximately finite dimensionai factors 87 Section 4. Outer conjugacy of automorphisms of strongly stable factors 92 Section 5. Injective factors of type IIIë, 0 ë 1 97 References 101 iii
Previous Page Next Page