**Memoirs of the American Mathematical Society**

1997;
107 pp;
Softcover

MSC: Primary 47; 46;

Print ISBN: 978-0-8218-0557-2

Product Code: MEMO/126/602

List Price: $47.00

Individual Member Price: $28.20

**Electronic ISBN: 978-1-4704-0187-0
Product Code: MEMO/126/602.E**

List Price: $47.00

Individual Member Price: $28.20

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

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*Igor Fulman*

In this book, the author introduces and studies the construction of the crossed product of a von Neumann algebra \(M = \int _X M(x)d\mu (x)\) by an equivalence relation on \(X\) with countable cosets. This construction is the generalization of the construction of the crossed product of an abelian von Neumann algebra by an equivalence relation introduced by J. Feldman and C. C. Moore. Many properties of this construction are proved in the general case. In addition, the generalizations of the Spectral Theorem on Bimodules and of the theorem on dilations are proved.

#### 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

#### Readership

Graduate students and research mathematicians interested in operator algebras.