On k-smoothness of operators between Banach spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911985791139840 |
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| author | Sain, Debmalya Sohel, Shamim Paul, Kallol |
| author_facet | Sain, Debmalya Sohel, Shamim Paul, Kallol |
| contents | We explore the $k$-smoothness of bounded linear operators between Banach spaces, using the newly introduced notion of index of smoothness. The characterization of the $k$-smoothness of operators between Hilbert spaces follows as a direct consequence of our study. We also investigate the $k$-smoothness of operators between polyhedral Banach spaces. In particular, we show that the $k$-smoothness of rank $1$ operators between polyhedral spaces depends heavily on the dimension of the corresponding spaces rather than the geometry of the spaces. The results obtained in this article generalize and improve upon the existing results in the $k$-smoothness of operators between Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On k-smoothness of operators between Banach spaces Sain, Debmalya Sohel, Shamim Paul, Kallol Functional Analysis Primary 46B20, Secondary 47B01, 47L05 We explore the $k$-smoothness of bounded linear operators between Banach spaces, using the newly introduced notion of index of smoothness. The characterization of the $k$-smoothness of operators between Hilbert spaces follows as a direct consequence of our study. We also investigate the $k$-smoothness of operators between polyhedral Banach spaces. In particular, we show that the $k$-smoothness of rank $1$ operators between polyhedral spaces depends heavily on the dimension of the corresponding spaces rather than the geometry of the spaces. The results obtained in this article generalize and improve upon the existing results in the $k$-smoothness of operators between Banach spaces. |
| title | On k-smoothness of operators between Banach spaces |
| topic | Functional Analysis Primary 46B20, Secondary 47B01, 47L05 |
| url | https://arxiv.org/abs/2407.19455 |