Sharper bounds for the numerical radius

Abstract

In this paper, we discuss and present new sharp inequalities for the numerical radii of Hilbert space operators. In particular, if A and B are bounded linear operators on a Hilbert space, we present new upper bounds for . The main tool to obtain our results is using block matrix techniques. Among many interesting results, and as an application of the new inequalities, we obtain the following bound for the numerical radius of an operator T, where , , and denote the numerical radius, the usual operator norm, and the absolute value operator, respectively. Other difference inequalities will be presented too.