Bounds for the Davis-Wielandt radius of bounded linear operators

Abstract

We obtain upper and lower bounds for the Davis-Wielandt radius of bounded linear operators defined on a complex Hilbert space, which improve on the existing ones. We also obtain bounds for the Davis-Wielandt radius of operator matrices. We determine the exact value of the Davis-Wielandt radius of two special type of operator matrices $\left(\begin{array}{ccc}I& B0& 0\end{array}\right)$ and $\left(\begin{array}{ccc}0& AB& 0\end{array}\right)$, where $A,B\in \mathcal{B}(\mathcal{H})$, $I$ and $0$ are the identity operator and the zero operator on $\mathcal{H},$ respectively. Finally we obtain bounds for the Davis-Wielandt radius of operator matrices of the form $\left(\begin{array}{ccc}A& B0& C\end{array}\right),$ where $A,B,C\in \mathcal{B}(\mathcal{H}).$

20 pages