Some inequalities of Hölder type for quadratic weighted geometric mean of bounded linear operators in Hilbert spaces

Abstract

In this paper, we consider the quadratic weighted geometric meanfor bounded linear operators T, V in the Hilbert space H with T invertible and . Using the celebrated McCarthy’s inequality we show thatfor any where p, with We also provide some norm inequalities such asfor any n-tuples of invertible operators and any n-tuple of positive weights .