Bounds for the Davis-Wielandt radius of bounded linear operators
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913466027081728 |
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| author | Bhunia, Pintu Bhanja, Aniket Bag, Santanu Paul, Kallol |
| author_facet | Bhunia, Pintu Bhanja, Aniket Bag, Santanu Paul, Kallol |
| contents | 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 $A,B, C\in \mathcal{B}(\mathcal{H}).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_04389 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Bounds for the Davis-Wielandt radius of bounded linear operators Bhunia, Pintu Bhanja, Aniket Bag, Santanu Paul, Kallol Functional Analysis Primary 47A12, Secondary 47A30, 47A50 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 $A,B, C\in \mathcal{B}(\mathcal{H}).$ |
| title | Bounds for the Davis-Wielandt radius of bounded linear operators |
| topic | Functional Analysis Primary 47A12, Secondary 47A30, 47A50 |
| url | https://arxiv.org/abs/2006.04389 |