Generalizations of Jensen’s operator inequality for convex functions to normal operators

Abstract

In this article, we generalize a well-known operator version of Jensen’s inequality to normal operators. The main techniques employed here are the spectral theory for bounded normal operators on a Hilbert space, and different Jensen-type inequalities. We emphasize the application of a vector version of Jensen’s inequality. By applying our results, some classical inequalities obtained for self-adjoint operators can also be extended.