Reverse cauchy - Schwarz inequalities for positive C*-valued sesquilinear forms

Abstract

We prove two new reverse Cauchy-Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C* -algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy-Schwarz inequality due to G. Pólya and G. Szegö.