Diagonalization and representation results for nonpositive sesquilinear form measures

Abstract

We study decompositions of operator measures and more general sesquilinear form measures $E$ into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent $E$ as a trace class valued measure of bounded variation on a new Hilbert space related to $E$. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.

J. Math. Anal. Appl., in press

References in corpus (1)

• Positive sesquilinear form measures and generalized eigenvalue expansions

Cited by in corpus (1)

• Modules, completely positive maps, and a generalized KSGNS construction