On generalized Davis-Wielandt radius inequalities of semi-Hilbertian space operators

Abstract

Let $A$ be a positive (semidefinite) operator on a complex Hilbert space $\mathcal{H}$ and let $\mathbb{A}=\left(\begin{array}{ccc}A& OO& A\end{array}\right).$ We obtain upper and lower bounds for the $A$-Davis-Wielandt radius of semi-Hilbertian space operators, which generalize and improve on the existing ones. We also obtain upper bounds for the $\mathbb{A}$-Davis-Wielandt radius of $2\times 2$ operator matrices. Finally, we determine the exact value for the $\mathbb{A}$-Davis-Wielandt radius of two operator matrices $\left(\begin{array}{cc}I& X\\ 0& 0\end{array}\right)$ and $\left(\begin{array}{cc}0& X\\ 0& 0\end{array}\right)$, where $X$ is a semi-Hilbertian space operator.

19 pages