Orlicz extension of Numerical radius inequalities

Abstract

In this paper, we achieve new and improved numerical radius inequalities of operators defined on a Hilbert space by using Orlicz function and Hermite-Hadamard inequality. The upper bounds of various inequalities involving numerical radii have been obtained. Finally, we compute an upper bound of the numerical radius for block matrices of the form $\left[\begin{array}{cc}O& P\\ Q& O\end{array}\right]$, where $P,Q$ are any bounded linear operators on a Hilbert space.

arXiv commentPreliminary version. Title, Abstract and Main results have been modified. 20 pages