# Characterizations of certain means of positive operators

## TL;DR

This paper provides new characterizations of various operator means, including quasi-arithmetic and Kubo-Ando geometric means, within the framework of positive definite operators on Hilbert spaces and C*-algebras.

## Contribution

It introduces novel characterizations for quasi-arithmetic and Kubo-Ando geometric means in the context of positive operators and non-commutative C*-algebras.

## Key findings

- Characterizations of quasi-arithmetic operator means including arithmetic and harmonic means.
- Characterization of Kubo-Ando geometric mean on non-commutative C*-algebras.
- Extension of mean characterizations to the positive definite cone of Hilbert space operators.

## Abstract

In this paper we present some characterizations for quasi-arithmetic operator means (among them the arithmetic and harmonic means) on the positive definite cone of the full algebra of Hilbert space operators, and also for the Kubo-Ando geometric mean on the positive definite cone of a general non-commutative $C^*$-algebra.