Transforms on operator monotone functions

TL;DR

This paper investigates a specific class of functions derived from operator monotone functions, proving their operator monotonicity, which advances understanding of functional transformations in operator theory.

Contribution

It introduces and proves the operator monotonicity of a new class of functions constructed from operator monotone functions, expanding the theoretical framework.

Findings

Proves operator monotonicity of the new function class

Extends the theory of operator monotone functions

Provides a basis for further functional analysis in operator theory

Abstract

For an operator monotone function $f(t)$ on the positive real line, we show the operator monotonicity of the type of the functions $(t-a)(t-b)/(f(t)-f(a))(f^\sharp(t)-f^\sharp(b))$.