Crossed products of von Neumann algebras by equivalence relations and their subalgebras

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.