# Ando-Hiai type inequalities for operator means and operator perspectives

## TL;DR

This paper advances the theory of operator means and perspectives by refining inequalities, introducing new results, and extending concepts to non-invertible operators, with implications for operator analysis.

## Contribution

It provides improved Ando-Hiai inequalities, new operator perspective inequalities, and extends the operator perspective framework to non-invertible positive operators.

## Key findings

- Enhanced Ando-Hiai inequalities for operator means
- New inequalities for operator perspectives
- Extension of operator perspectives to non-invertible operators

## Abstract

We improve the existing Ando-Hiai inequalities for operator means and present new ones for operator perspectives in several ways. We also provide the operator perspective version of the Lie-Trotter formula and consider the extension problem of operator perspectives to non-invertible positive operators.