Lieb type convexity for positive operator monotone decreasing functions

TL;DR

This paper establishes Lieb type convexity and concavity results for trace functionals involving positive operator monotone decreasing functions, extending previous work on power functions.

Contribution

It generalizes Lieb's convexity results to a broader class of functions, including monotone decreasing and concave functions, advancing the theoretical understanding of trace functionals.

Findings

Proves Lieb type convexity for certain trace functionals

Establishes Lieb type concavity for related trace functionals

Provides a partial generalization of Hiai's work on power functions

Abstract

We prove Lieb type convexity and concavity results for trace functionals associated with positive operator monotone (decreasing) functions and certain monotone concave functions. This gives a partial generalization of Hiai's recent work on trace functionals associated with power functions.