# Strengthened convexity of positive operator monotone decreasing functions

## TL;DR

This paper establishes a stronger convexity property for positive operator monotone decreasing functions, extending previous results to more general positive maps and functional calculus.

## Contribution

It generalizes existing convexity results for operator monotone decreasing functions to include arbitrary positive maps and broader functional calculus.

## Key findings

- Proves a strengthened convexity property for these functions.
- Extends previous work by Ando and Hiai to more general settings.
- Broadens the applicability of convexity results in operator theory.

## Abstract

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.