Orlicz extension of Numerical radius inequalities

TL;DR

This paper introduces new bounds for the numerical radius of operators on Hilbert spaces using Orlicz functions and Hermite-Hadamard inequality, including bounds for block matrices.

Contribution

It extends numerical radius inequalities by applying Orlicz functions and Hermite-Hadamard inequality, providing improved bounds and specific results for block matrices.

Findings

Derived new upper bounds for numerical radii of operators.

Established bounds for block matrices with off-diagonal operators.

Enhanced existing inequalities with Orlicz function techniques.

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 $\begin{bmatrix}O & P\\Q & O \end{bmatrix}$, where $P, Q$ are any bounded linear operators on a Hilbert space.