Noncommutative Perspectives of Operator Monotone Functions in Hilbert Spaces

TL;DR

This paper explores identities related to noncommutative perspectives of operator monotone functions in Hilbert spaces, with applications to operator means and entropy, advancing understanding in operator theory.

Contribution

It introduces new identities for noncommutative perspectives and applies them to operator geometric mean and entropy, offering novel insights.

Findings

Identities for noncommutative perspectives derived

Applications to weighted operator geometric mean demonstrated

Results enhance understanding of operator entropy

Abstract

Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.