Abstract
The aim of this paper is to provide new upper bounds of omega (T), which denotes the numerical radius of a bounded operator T on a Hilbert space (H, <middot, middot>). We show the Acz & eacute;l inequality in terms of the operator |T|. Next, we give certain inequalities about the A-numerical radius omega(A)(T) and the A-operator seminorm ||T||(A) of an operator T. We also present several results related to the A-numerical radius of 2 x 2 block matrices of semi-Hilbert space operators, by using symmetric 2 x 2 block matrices.