# Crossed Products of von Neumann Algebras by Equivalence Relations and Their Subalgebras

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*Igor Fulman*

#### Table of Contents

# Table of Contents

## Crossed Products of von Neumann Algebras by Equivalence Relations and Their Subalgebras

- Contents vii8 free
- 1 Introduction 112 free
- 2 Preliminaries 314 free
- 3 Unitary realization of α([sub(y,x)]) 516
- 4 Construction of M[sup(∇)] 617
- 5 Coordinate representation of elements of M 718
- 6 The expectation E 1021
- 7 Coordinates in M[sup(∇)] 1122
- 8 The expectation E' 1425
- 9 Tomita…Takesaki theory for M and M[sup(∇)] 1526
- 10 I(M)–automorphisms of M 2233
- 11 Flows of automorphisms 2637
- 12 The Feldman–Moore–type structure theorem 3243
- 13 Isomorphisms of crossed products 5263
- 14 Bimodules and subalgebras of M 6273
- 15 Spectral theorem for bimodules 7081
- 16 Analytic algebra of a flow of automorphisms 8192
- 17 Properties of M 8394
- 18 Hyperfiniteness and dilations 8596
- 19 The construction of Yamanouchi 93104
- 20 Examples and particular cases 99110