Inequalities for Quadratic Operator Perspective of Convex Functions and Bounded Linear Operators in Hilbert Spaces

TL;DR

This paper introduces the quadratic operator perspective for convex functions on positive semi-axis, generalizing existing means and entropies, and establishes related inequalities with applications in operator theory.

Contribution

It proposes a new quadratic operator perspective concept that extends the quadratic weighted operator geometric mean and relative operator entropy, along with derived inequalities.

Findings

Established inequalities for the quadratic operator perspective of convex functions

Generalized quadratic weighted operator geometric mean and entropy

Provided applications in operator inequalities

Abstract

In this paper we introduce the concept of quadratic operator perspective for a continuous function {\Phi} defined on the positive semi-axis of real numbers. This generalize the quadratic weighted operator geometric mean and the quadratic relative operator entropy. Some inequalities for this perspective of convex functions are established. Applications for quadratic weighted operator geometric mean and quadratic relative operator entropy are also provided.