Bounds for the Davis-Wielandt radius of bounded linear operators

Pintu Bhunia, Aniket Bhanja, Santanu Bag, Kallol Paul

Published 2020-06-08Version 1

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. Finally we compute the exact value of the Davis-Wielandt radius of two special operator matries $\left(\begin{array}{cc} I & B 0 & 0 \end{array}\right)$ and $\left(\begin{array}{cc} 0 & B 0 & 0 \end{array}\right),$ where $B$ is a bounded linear operator on a complex Hilbert space and $I$ is the identity operator on the same Hilbert space.