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 [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].

Application of Operator Matrices of 2x2 of Berezin Radius Inequality

“…The numeric range of an operator has some interesting properties, such as the closure of the numeric range of an operator's spectrum. For basic information about this theory, we can give [1,2,3,7,17] and its references.…”