Memoirs of the American Mathematical Society 1997; 107 pp; softcover Volume: 126 ISBN10: 0821805576 ISBN13: 9780821805572 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/126/602
 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. Readership Graduate students and research mathematicians interested in operator algebras. Table of Contents  Introduction
 Preliminaries
 Unitary realization of \(\alpha _{(y,x)}\)
 Construction of \(\tilde M^\nabla\)
 Coordinate representation of elements of \(\tilde M\)
 The expectation \(E\)
 Coordinates in \(\tilde M^\nabla\)
 The expectation \(E'\)
 TomitaTakesaki theory for \(\tilde M\) and \(\tilde M^\nabla\)
 \(I(M)\) automorphisms of \(\tilde M\)
 Flows of automorphisms
 The FeldmanMooretype structure theorem
 Isomorphisms of crossed products
 Bimodules and subalgebras of \(\tilde M\)
 Spectral theorem for bimodules
 Analytic algebra of a flow of automorphisms
 Properties of \(\tilde M\)
 Hyperfiniteness and dilations
 The construction of Yamanouchi
 Examples and particular cases
