New upper bounds for the $q$-numerical radius of Hilbert space operators

TL;DR

This paper presents new upper bounds for the $q$-numerical radius of operators on Hilbert spaces, refining existing bounds and deriving inequalities for products, commutators, and operator matrices.

Contribution

It introduces novel upper bounds for the $q$-numerical radius, improving upon previous results and extending inequalities to products, commutators, and matrices.

Findings

Refined upper bounds for the $q$-numerical radius.

Derived inequalities for products and commutators.

Established bounds for $2 imes 2$ operator matrices.

Abstract

This article introduces several new upper bounds for the $q$-numerical radius of bounded linear operators on complex Hilbert spaces. Our results refine some of the existing upper bounds in this field. The $q$-numerical radius inequalities of products and commutators of operators follow as special cases. Finally, some new inequalities for the $q$-numerical radius of $2 \times 2$ operator matrices are established.