Comparison of Completely Positive Maps on Hilbert C*-Modules

TL;DR

This paper introduces a new preorder relation among operator-valued completely positive maps on Hilbert C*-modules and characterizes it using the Stinespring construction, advancing the understanding of their structural properties.

Contribution

It defines and characterizes a preorder relation on completely positive maps on Hilbert C*-modules using the Stinespring construction, providing new insights into their structure.

Findings

Established a preorder relation among completely positive maps.

Characterized the relation via the Stinespring construction.

Enhanced understanding of operator-valued completely positive maps.

Abstract

We introduce a preorder relation in the collection of all operator valued completely positive maps on a full Hilbert C*-module and characterize this relation in terms of the Stinespring construction associated to each completely positive map.