$A$-Davis-Wielandt Radius Bounds of Semi-Hilbertian Space Operators
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917738137518080 |
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| author | Guesba, Messaoud Barik, Somdatta Bhunia, Pintu Paul, Kallol |
| author_facet | Guesba, Messaoud Barik, Somdatta Bhunia, Pintu Paul, Kallol |
| contents | Consider $\mathcal{H}$ is a complex Hilbert space and $A$ is a positive operator on $\mathcal{H}.$ The mapping $\langle\cdot,\cdot\rangle_A: \mathcal{H}\times \mathcal{H} \to \mathbb {C}$, defined as $\left\langle y,z\right\rangle_{A}=\left\langle Ay,z\right\rangle $ for all $y,z$ $\in $ ${\mathcal{H}}$, induces a seminorm $ \left\Vert \cdot\right\Vert_{A}$. The $A$-Davis-Wielandt radius of an operator $S$ on $\mathcal{H}$ is defined as $dω_{A}\left( S\right) =\sup \left\{ \sqrt{\left\vert \left\langle Sz,z\right\rangle_{A}\right\vert ^{2}+\left\Vert Sz\right\Vert_{A}^{4}} :\left\Vert z\right\Vert_{A}=1\right\} \text{.} $ We investigate some new bounds for $dω_{A}\left( S\right)$ which refine the existing bounds. We also give some bounds for the $2\times 2$ off-diagonal block matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $A$-Davis-Wielandt Radius Bounds of Semi-Hilbertian Space Operators Guesba, Messaoud Barik, Somdatta Bhunia, Pintu Paul, Kallol Functional Analysis 47A05, 47A12, 47A30, 47B15 Consider $\mathcal{H}$ is a complex Hilbert space and $A$ is a positive operator on $\mathcal{H}.$ The mapping $\langle\cdot,\cdot\rangle_A: \mathcal{H}\times \mathcal{H} \to \mathbb {C}$, defined as $\left\langle y,z\right\rangle_{A}=\left\langle Ay,z\right\rangle $ for all $y,z$ $\in $ ${\mathcal{H}}$, induces a seminorm $ \left\Vert \cdot\right\Vert_{A}$. The $A$-Davis-Wielandt radius of an operator $S$ on $\mathcal{H}$ is defined as $dω_{A}\left( S\right) =\sup \left\{ \sqrt{\left\vert \left\langle Sz,z\right\rangle_{A}\right\vert ^{2}+\left\Vert Sz\right\Vert_{A}^{4}} :\left\Vert z\right\Vert_{A}=1\right\} \text{.} $ We investigate some new bounds for $dω_{A}\left( S\right)$ which refine the existing bounds. We also give some bounds for the $2\times 2$ off-diagonal block matrices. |
| title | $A$-Davis-Wielandt Radius Bounds of Semi-Hilbertian Space Operators |
| topic | Functional Analysis 47A05, 47A12, 47A30, 47B15 |
| url | https://arxiv.org/abs/2407.21639 |