Equivalence relations among some inequalities on operator means

TL;DR

This paper explores inequalities involving various operator means for multiple operators, including geometric, log-Euclidean, and logarithmic means, expanding understanding of their relationships.

Contribution

It introduces new inequalities and relations among different operator means for more than three operators, including ALM, BMP, log-Euclidean, and logarithmic means.

Findings

Established equivalence relations among inequalities of operator means.

Extended inequalities to multiple operators beyond three.

Analyzed properties of log-Euclidean and logarithmic means.

Abstract

We will consider about some inequalities on operator means for more than three operators, for instance, ALM and BMP geometric means will be considered. Moreover, log-Euclidean and logarithmic means for several operators will be treated.