Matrix KSGNS construction and a Radon--Nikodym type theorem

Abstract

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert $A$-modules over locally $C^{\ast }$-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the Radon--Nikodym theorem for this type of completely positive $n\times n$ matrices.

17 pages; The paper was revised and some material is added to it. To appear in Indag. Math

References in corpus (1)

• KSGNS type construction for $\alpha$-completely positive maps on Krein $C^{\ast }$-modules