On local preservation of orthogonality and its application to isometries
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914911030870016 |
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| author | Sain, Debmalya Manna, Jayanta Paul, Kallol |
| author_facet | Sain, Debmalya Manna, Jayanta Paul, Kallol |
| contents | We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the concerned spaces. In particular, it is shown that such a study is related to the preservation of k-smoothness and the extremal properties of the unit ball of a Banach space. As an application of the results obtained in this direction, we obtain a refinement of the well-known Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On local preservation of orthogonality and its application to isometries Sain, Debmalya Manna, Jayanta Paul, Kallol Functional Analysis 46B20, 47B01, 47L05 We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the concerned spaces. In particular, it is shown that such a study is related to the preservation of k-smoothness and the extremal properties of the unit ball of a Banach space. As an application of the results obtained in this direction, we obtain a refinement of the well-known Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $ |
| title | On local preservation of orthogonality and its application to isometries |
| topic | Functional Analysis 46B20, 47B01, 47L05 |
| url | https://arxiv.org/abs/2407.08900 |