On Variance and Covariance for Bounded Linear Operators

Abstract

In this thesis we have studied Covariance and Variance for bounded linear operators on a complex Hilbert space, where we focus our study on Covariance-Variance inequality(C-V inequality)and its applications. We apply (C-V inequality) to prove some improvements on some known inequalities like Bernistein, Heinz-Kato-Furuta and Reid inequalities. We introduce Furuta inequality and proved an extension of Reid inequality. Finally we use the C-V inequality to prove several inequalities equivalent to Furuta inequality.