Further Inequalities for the Weighted Numerical Radius of Operators

Abstract

This paper deals with the so-called A-numerical radius associated with a positive (semi-definite) bounded linear operator A acting on a complex Hilbert space H. Several new inequalities involving this concept are established. In particular, we prove several estimates for 2×2 operator matrices whose entries are A-bounded operators. Some of the obtained results cover and extend well-known recent results due to Bani-Domi and Kittaneh. In addition, several improvements of the generalized Kittaneh estimates are obtained. The inequalities given by Feki in his work represent a generalization of the inequalities given by Kittaneh. Some refinements of the inequalities due to Feki are also presented.