A SPATIAL CHARACTERIZATION OF co CONDITIONAL EXPECTATIONS ON VON NEUMANN ALGEBRAS

摘要

Representations of the predual of von Neumann algebras as spaces of densely defined sesquilinar forms on the Hilbert space on which the von Neumann algebras itself operate are taken as a setting on which to extend m-conditional expectations. This allows us to give a spatial characterization of co-conditional expectations through a properly which is a natural generalization of a characterising property of norm one projections on von Neumann algebras.