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
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