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arXiv · 2006.05069

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

Aniket Bhanja·Pintu Bhunia·Kallol Paul
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Abstract

Let $A$ be a positive (semidefinite) operator on a complex Hilbert space $\mathcal{H}$ and let $\mathbb{A}=\left(\begin{array}{cc} A & O O & A \end{array}\right).$ 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.

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Aniket Bhanja, Pintu Bhunia, Kallol Paul. 2020-06-09. On generalized Davis-Wielandt radius inequalities of semi-Hilbertian space operators. https://arxiv.org/abs/2006.05069

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