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arXiv · 2006.04389

Bounds for the Davis-Wielandt radius of bounded linear operators

Pintu Bhunia·Aniket Bhanja·Santanu Bag·Kallol Paul
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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 $\left(\begin{array}{cc} I & B 0 & 0 \end{array}\right)$ and $\left(\begin{array}{cc} 0 & A B & 0 \end{array}\right)$, 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 $\left(\begin{array}{cc} A& B 0 & C \end{array}\right),$ where $A,B, C\in \mathcal{B}(\mathcal{H}).$

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Pintu Bhunia, Aniket Bhanja, Santanu Bag, Kallol Paul. 2020-06-08. Bounds for the Davis-Wielandt radius of bounded linear operators. https://doi.org/10.1007/s43034-020-00102-9

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