A Radon-Nikodym theorem for CP-maps on Hilbert pro-C*-modules

TL;DR

This paper develops a Radon-Nikodym theorem for completely positive maps between Hilbert modules over pro-C*-algebras, extending the theoretical framework of operator algebras and module theory.

Contribution

It introduces an equivalence relation and a preorder on CP-maps over pro-C*-algebras, and analyzes their Stinespring's representations to establish a Radon-Nikodym type theorem.

Findings

Established an equivalence relation on CP-maps

Analyzed Stinespring's construction for equivalent maps

Proved a Radon-Nikodym type theorem for these maps

Abstract

We introduce an equivalence relation on the set of all completely positive maps between Hilbert modules over pro-C*-algebras and analyze the Stinespring's construction for equivalent completely positive maps. We then give a preorder relation in the collection of all completely positive maps between Hilbert modules over pro-C*-algebras and obtain a Radon-Nikodym type theorem.