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

TL;DR

This paper establishes new reverse Cauchy--Schwarz inequalities for positive C*-valued sesquilinear forms, leading to improved inequalities in norm and integral contexts, with applications to classical inequalities.

Contribution

It introduces novel additive and multiplicative reverse inequalities for positive C*-valued sesquilinear forms, enhancing existing bounds like those of Polya and Szego.

Findings

Derived new reverse inequalities for C*-valued forms

Improved classical inequalities with tighter bounds

Applied results to norm and integral inequalities

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 Polya and G. Szego.