Operator extensions of Hua's inequality

TL;DR

This paper extends Hua's inequality within the framework of Hilbert C*-modules, introducing new operator inequalities and generalizations without relying on convexity, and linking operator convexity to Hua's inequality.

Contribution

It provides novel operator extensions of Hua's inequality in Hilbert C*-modules, including a Jensen inequality and an operator Hua's inequality related to operator convex functions.

Findings

Extended Hua's inequality in pre-Hilbert C*-modules

Derived a Jensen inequality in Hilbert C*-modules

Established an operator Hua's inequality equivalent to operator convexity

Abstract

We give an extension of Hua's inequality in pre-Hilbert $C^*$-modules without using convexity or the classical Hua's inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert $C^*$-modules, another extension of Hua's inequality is obtained. We also present an operator Hua's inequality, which is equivalent to operator convexity of given continuous real function.