Refinements of Some Numerical Radius Inequalities for Hilbert Space Operators

Abstract

Some power inequalities for the numerical radius based on the recent Dragomir extension of Furuta's inequality are established. Some particular cases are also provided. Moreover, we get an improvement of the H\"older-McCarthy operator inequality in the case when $r\geq 1$ and refine generalized inequalities involving powers of the numerical radius for sums and products of Hilbert space operators.