A convex-block approach for numerical radius inequalities

TL;DR

This paper introduces a convex-block method to derive new refined inequalities for the numerical radius of Hilbert space operators, enhancing understanding of operator norms, Cartesian parts, and transformations.

Contribution

It presents a novel convex-block approach that improves existing numerical radius inequalities and provides new bounds involving operator products and transforms.

Findings

New refined inequalities for numerical radius of operators

Comparisons among operator norms, Cartesian parts, and radii

Bounds involving the Aluthge transform and operator products

Abstract

This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their Cartesian parts, their numerical radii, the numerical radius of the product of two operators, and the Aluthge transform.