Operator extensions of Hua's inequality

Abstract

We give an extension of Hua's inequality in pre-Hilbert $C^{\ast }$-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 $C^{\ast }$-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.

arXiv comment12 Pages, To appear in Linear Alg. Appl. (LAA)