Characterization of k-smoothness of operators defined between infinite-dimensional spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914910271700992 |
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| author | Mal, Arpita Sey, Subhrajit Paul, Kallol |
| author_facet | Mal, Arpita Sey, Subhrajit Paul, Kallol |
| contents | We characterize $k-$smoothness of bounded linear operators defined between infinite-dimensional Hilbert spaces. We study the problem in the setting of both finite and infinite-dimensional Banach spaces. We also characterize $k-$smoothness of operators on some particular spaces, namely $\mathbb{L}(\mathbb{X},\ell_{\infty}^n),~\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{X}$ is a finite-dimensional Banach space and $\mathbb{Y}$ is a two-dimensional Banach space. As an application, we characterize extreme contractions on $\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{Y}$ is a two-dimensional polygonal Banach space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_12628 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Characterization of k-smoothness of operators defined between infinite-dimensional spaces Mal, Arpita Sey, Subhrajit Paul, Kallol Functional Analysis Primary 46B20, Secondary 47L05 We characterize $k-$smoothness of bounded linear operators defined between infinite-dimensional Hilbert spaces. We study the problem in the setting of both finite and infinite-dimensional Banach spaces. We also characterize $k-$smoothness of operators on some particular spaces, namely $\mathbb{L}(\mathbb{X},\ell_{\infty}^n),~\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{X}$ is a finite-dimensional Banach space and $\mathbb{Y}$ is a two-dimensional Banach space. As an application, we characterize extreme contractions on $\mathbb{L}(\ell_{\infty}^3,\mathbb{Y}),$ where $\mathbb{Y}$ is a two-dimensional polygonal Banach space. |
| title | Characterization of k-smoothness of operators defined between infinite-dimensional spaces |
| topic | Functional Analysis Primary 46B20, Secondary 47L05 |
| url | https://arxiv.org/abs/2007.12628 |