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

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.