On some elementary properties of the crossed products of von Neumann algebras

Abstract

Many mathematical models would be employed by yon Neumann in his investigation on the rings of operators. The theories of quantum mechanics, infinite groups, integration, measure preserving transformations and so on would be found among them. However, the classical theory of simple algebras would play an eminent rSle in his monumental "rings of operators" series, since the von Neumann algebras are recognized by himself as an infinite dimensional hyper- complex numbers in his earlier paper.