Banach bimodule-valued positive maps: Inequalities and induced representations

TL;DR

This paper investigates representations induced by positive maps valued in Banach bimodules, deriving new inequalities and expanding understanding of their structure in operator algebra contexts.

Contribution

It introduces a general framework for induced representations via positive sesquilinear maps into Banach bimodules, with new inequalities for these maps.

Findings

Derived new inequalities for positive and completely positive maps.

Extended the theory to maps into spaces of trace-class and bounded operators.

Provided a unified approach to representations in operator algebra settings.

Abstract

In this paper, we consider representations induced by general positive and completely positive sesquilinear maps with values in ordered Banach bimodules, such as the space of trace-class operators and the spaces of bounded linear operators from a von Neumann algebra into the dual of another von Neumann algebra. Also, we deduce some new inequalities for these maps.