On the Davis-Wielandt radius inequalities of Hilbert space operators

TL;DR

This paper introduces new bounds and generalizations for the Davis-Wielandt radius of Hilbert space operators, including matrix cases and an extension to the Euclidean operator radius, advancing the theoretical understanding of these operator measures.

Contribution

The paper provides novel upper and lower bounds for the Davis-Wielandt radius and extends its concept to the Euclidean operator radius, including matrix cases.

Findings

New bounds for the Davis-Wielandt radius established

Generalizations of existing results presented

Bounds for operator matrices derived

Abstract

In this work, some new upper and lower bounds of the Davis-Wielandt radius are introduced. Generalizations of some presented results are obtained. Some bounds of the Davis-Wielandt radius for $n\times n$ operator matrices are established. An extension of the Davis-Wielandt radius to the Euclidean operator radius is introduced.