Geometric properties for a class of deformed trace functions

TL;DR

This paper explores geometric aspects of a class of trace functions built from deformed logarithms and exponentials, extending previous results in the field and highlighting their potential significance.

Contribution

It introduces and analyzes geometric properties of deformed trace functions, extending earlier theoretical results by Epstein, Hiai, Carlen, and Lieb.

Findings

Identification of geometric properties of deformed trace functions

Extension of previous theoretical results in the literature

Potential applications in mathematical physics and operator theory

Abstract

We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular to extend earlier results of Epstein, Hiai, Carlen and Lieb.