On the Cauchy-Schwarz inequality and its reverse in semi-inner product C*-modules

Abstract

There are many known Cauchy-Schwarz-type inequalities which are valid in different frameworks. In this paper we consider the $A$-valued Cauchy-Schwarz inequality and its reverse in a semi-inner product $A$-module over the $C^*$-algebra $A$. Some remarks on the $A$-valued Cauchy-Schwarz inequality in a semi-inner product $A$-module over the $H^*$-algebra $A$ are also given.