Further bounds on $q$-numerical radius of Hilbert space operators

TL;DR

This paper introduces new inequalities for the $q$-numerical radius of operators and matrices, providing bounds and relations that enhance understanding of operator behavior in Hilbert spaces.

Contribution

The paper presents novel inequalities involving the $q$-numerical radius, including bounds for operators and operator matrices, utilizing Buzano inequality.

Findings

Established new lower and upper bounds for the $q$-numerical radius.

Derived inequalities for $2\times 2$ operator matrices.

Applied Buzano inequality to obtain $q$-numerical radius inequalities.

Abstract

In this article, we developed a series of new inequalities involving the $q$-numerical radius for operators and $2\times 2$ operator matrices. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of operators. Additionally, we established $q$-numerical radius inequalities for operators via Buzano inequality.