Norm inequalities related to Heinz and Heron operator means

TL;DR

This paper introduces new inequalities comparing Heinz and Heron operator means, refining existing results and employing contractive maps to improve bounds for unitarily invariant norms.

Contribution

It provides novel comparisons and refinements of inequalities between Heinz and Heron means using contractive maps, advancing the theoretical understanding of these operator means.

Findings

Improved inequalities between Heinz and Heron means.

Refinements for unitarily invariant norms.

Enhanced bounds using contractive maps.

Abstract

In this article we present some new comparisons between the Heinz and Heron operator means, which improve some recent results known from the literature. We derive some refinements of these inequalities for unitarily invariant norms with the help of the contractive maps.