Diagonal measure of a positive definite bimeasure

Abstract

Introduction. It has recently been shown [8] (cf. [2], [10], [11]) that any bounded vector measure with values in a Hilbert space can be obtained as an orthogonal projection of a bounded orthogonally scattered vector measure with values in a larger Hilbert space H . In this paper we characterize the class T of all O = bounded Hilbert space valued vector measures F: F § H for which there exist a : F + H and Hilbert space Ho, a bounded orthogonally scattered vector measure F ~ _ o a bounded linear mapping A: H + H with a bounded inverse such that O