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.
"Generalizations of Jensen’s operator inequality for convex functions to normal operators." Ann. Funct. Anal. 9 (4) 566 - 573, November 2018. https://doi.org/10.1215/20088752-2018-0002