Perspectives and completely positive maps

TL;DR

This paper extends operator inequalities and convexity theorems from two variables to multiple variables using completely positive maps, with applications in operator means.

Contribution

It introduces a method to generalize known inequalities and convexity results from two to many variables via completely positive maps.

Findings

Extended operator inequalities to multiple variables.

Generalized Lieb-Ruskai's convexity theorem to n+1 variables.

Applied results to operator means of several variables.

Abstract

We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with applications in the theory of operator means of several variables. We also extend Lieb-Ruskai's convexity theorem from two to $ n+1 $ operator variables.