Numerical radius inequalities concerning with algebraic norms

TL;DR

This paper introduces a generalized numerical radius for Hilbert space operators, deriving bounds and inequalities involving operator products, with applications demonstrating the utility of these new bounds.

Contribution

It provides a new expression for the generalized numerical radius and establishes novel inequalities involving products of operators.

Findings

Derived bounds for the generalized numerical radius

Established inequalities involving operator products

Presented applications of the inequalities

Abstract

We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities involving the product of two operators. Applications of our inequalities are also provided.