General Upper Bounds for the Numerical Radii of Powers of Hilbert Space Operators

Abstract

In this paper, we will present several upper bounds for the numerical radii of a operator matrices. We use these bounds to generalize and improve some well-known numerical radius inequalities. We provide a refinement of an earlier numerical radius inequality due to (Bani-Domi & Kittaneh, 2021) [Norm and numerical radius inequalities for Hilbert space operators], (Bani-Domi & Kittaneh, 2021) [Refined and generalized numerical radius inequalities for operator matrices] and (Al-Dolat & Kittaneh, 2023) [Upper bounds for the numerical radii of powers of Hilbert space operators].