Stinespring's theorem for maps on Hilbert C*-modules

TL;DR

This paper extends Stinespring's theorem to maps on Hilbert C*-modules, proving the uniqueness of minimal representations and providing an illustrative example.

Contribution

It strengthens Asadi's analogue of Stinespring's theorem for Hilbert C*-modules and establishes the unitary equivalence of minimal representations.

Findings

Strengthened the analogue of Stinespring's theorem for Hilbert C*-modules.

Proved that any two minimal Stinespring representations are unitarily equivalent.

Provided an example illustrating the main theorem.

Abstract

We strengthen Mohammad B. Asadi's analogue of Stinespring's theorem for certain maps on Hilbert C*-modules. We also show that any two minimal Stinespring representations are unitarily equivalent. We illustrate the main theorem with an example.