Operator means deformed by a fixed point method

TL;DR

This paper investigates how operator and multivariate means of positive definite matrices can be deformed using a fixed point approach, ensuring the deformed means retain their fundamental properties.

Contribution

It introduces a fixed point method for deforming operator means, demonstrating that the deformed means remain within the class of operator means, especially focusing on weighted power mean deformations.

Findings

Deformation via fixed point preserves the operator mean structure.

Deformed means by weighted power means are explicitly characterized.

The method ensures the stability of operator means under deformation.

Abstract

By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means deformed by the weighted power means are particularly examined.