More on operator Bellman inequality

Abstract

We present a Bellman inequality involving operator means for operators acting on a Hilbert space. We also give some Bellman inequalities concerning sesquilinear forms. Finally, we re ne the Jensen's operator inequality and use it for obtaining a re nement of the Bellman operator inequality.

Keywords: Bellman inequality, operator mean, operator concavity, positive linear functional, Jensen's inequality

Quaestiones Mathematicae 37(2014), 9-17