Matrix inequalities from a two variables functional

TL;DR

This paper introduces new matrix inequalities derived from a two-variable log-convex norm functional, extending the Araki Log-majorization theorem through novel log-majorization techniques for positive linear maps and normal operators.

Contribution

It presents a new two-variable log-convex norm functional and extends the Araki Log-majorization theorem with unexpected matrix/operator inequalities.

Findings

Extended Araki Log-majorization theorem

Developed a new log-majorization for positive linear maps

Introduced a two-variable log-convex norm functional

Abstract

Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea and technical tool is a two variables log-convex norm functional (Theorem 1.2).