Measures on classes of subspaces affiliated with a von neumann algebra

Abstract

Let ℳ be a von Neumann algebra acting on a Hilbert space H and let S be a dense lineal in H that is affiliated with a von Neumann algebra ℳ. The "topological" definition of measures on the classes of orthoclosed and splitting subspaces of S affiliated with a von Neumann algebra ℳ is given and results on the relationships of these measures to measures on orthoprojections of the algebra ℳ are presented. © Springer Science+Business Media, LLC 2009.