Inequalities and Reverse Inequalities for the Joint <i>A</i>-Numerical Radius of Operators

Abstract

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius for d=1. Here, A is a positive operator on H. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated.

Keywords

• positive operator
• joint <i>A</i>-numerical radius
• Euclidean operator <i>A</i>-seminorm
• joint operator <i>A</i>-seminorm