A Commutator Approach to Buzano's Inequality


Maryam Khosravi, Roman Drnovšek, Mohammad Sal Moslehian




Using a $2x2$ 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.