Davis-Wielandt Radius of $2 \times 2$ Hilbert-Schmidt Operator Matrices

Document Type : Original Article

Authors

Mehdi Naimi ¹

Benharrat Mohammed ²

Hireche Faouzi ¹

¹ Universit\'e Abdelhamid Ibn Badis de Mostaganem Mostaganem 27000‎, ‎Alg\'erie

² Ecole Nationale Polytechnique d'Oran-Maurice Audin (Ex‎. ‎ENSET d'Oran), BP 1523 Oran-El M'naouar\\ 31000 Oran, Alg\'{e}rie

10.22034/kjm.2025.513686.3492

Abstract

In this article, we present the formula of the Davis–Wielandt radius for a Hilbert–Schmidt operator, and provide an alternative to the classical triangle inequality for the Davis–Wielandt radius of the sum of two Hilbert–Schmidt operators. Additionally, several bounds for the Davis–Wielandt radius of \(2 \times 2\) Hilbert–Schmidt operator matrices defined on \(\mathcal{H} \times \mathcal{H}\) are given. In particular, we focus on the estimation of this radius for specific matrices, such as diagonal and off-diagonal matrices.

Keywords

Davis–Wielandt radius

numerical radius

Hilbert-Schmidt norm

Subjects

• 47 Operator theory

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