A commutator approach to Buzano's inequality

Abstract

Using a 2×2 matrix trick, an inequality involving commutators of certain Hilbert space operators as an operator version of Buzano's inequality, which is in turn a generalization of the Cauchy-Schwarz inequality, is presented. Also a version of the inequality in the framework of Hilbert C*-modules is stated and a special case in the context of C*-algebras is presented.