FURTHER RESULTS ON JENSEN-TYPE INEQUALITIES

Abstract

In this paper, we establish some Jensen-type inequalities for continuous functions of self-adjoint operators on complex Hilbert spaces. Furthermore, using the Cartesian decomposition of an operator, we improve the known result due to Mond and Peˇcari´c. Some refinements of the H¨older-McCarthy inequality are given as well.

Keywords

• jensen’s inequality
• convex function
• synchronous (asynchronous) function
• self-adjoint operator