Bessel and Grüss type inequalities in inner product modules over Banach-algebras

Abstract

We give an analogue of the Bessel inequality and we state a simple formulation of the Grss type inequality in inner product C *-modules, which is a refinement of it. We obtain some further generalization of the Grss type inequalities in inner product modules over proper H *-algebras and unital Banach *-algebras for C *-seminorms and positive linear functionals. Copyright 2011 A. G. Ghazanfari and S. S. Dragomir.