A sufficient condition for global operator monotonicity for functions in several variables

TL;DR

This paper discusses conditions under which functions of several variables exhibit global operator monotonicity, building on previous work and providing additional insights into the mathematical properties involved.

Contribution

It offers new remarks and clarifications on sufficient conditions for global operator monotonicity for multivariable functions, extending prior results.

Findings

Provides additional remarks on sufficient conditions for operator monotonicity.

Clarifies the mathematical framework for multivariable operator functions.

Builds upon and extends previous results in the field.

Abstract

The note contains two remarks to the authors note (Mathematical Notes, Vol. 94, 2013, p. 154 -- 156; in Russian) which was also devoted to sufficient conditions of global operator monotonicity.