Stinespring type theorem for a finite family of maps on Hilbert C*-modules

TL;DR

This paper extends Stinespring's theorem to finite families of completely positive maps on Hilbert C*-modules, establishing unitary equivalence of minimal representations and broadening the theoretical framework.

Contribution

It introduces a Stinespring type theorem for multiple maps on Hilbert C*-modules, generalizing previous results and demonstrating the unitary equivalence of minimal representations.

Findings

Proved a Stinespring type theorem for finite families of maps.

Showed minimal representations are unitarily equivalent.

Extended the theory of completely positive maps on Hilbert C*-modules.

Abstract

The aim of this article is to extend the results of Asadi M.B, B.V.R. Bhat, G. Ramesh, K. Sumesh about completely positive maps on Hilbert C*-modules. We prove a Stinespring type theorem for a finite family of completely positive maps on Hilbert C*-modules. We also show that any two minimal Stinespring representations are unitarily equivalent.