PROBABILISTIC ASPECTS OF VON NEUMANN ALGEBRAS

Let G be a von Neumann Algebra, admitting a finite trace. It is shown that convergence in measure of a sequence of Normal Operators measurable with respect to G, is preserved by any continuous function (of the Complex Plane to itself). Then a Theorem on convergence in the mean is proved. Also obtained is a non-commutative generalization of the Kolmogorov-Gelfand-Yaglom Result on the information of one measure, relative to another measure, contained in a σ-field. © 1979.