On directional preservation of orthogonality and its application to isometries
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866912178132484096 |
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| author | Manna, Jayanta Mandal, Kalidas Paul, Kallol Sain, Debmalya |
| author_facet | Manna, Jayanta Mandal, Kalidas Paul, Kallol Sain, Debmalya |
| contents | We study the local preservation of Birkhoff-James orthogonality by linear operators between normed linear spaces, at a point and in a particular direction. We obtain a complete characterization of the same, which allows us to present refinements of the local preservation of orthogonality explored earlier. We also study the directional preservation of orthogonality with respect to certain special subspaces of the domain space, and apply the results towards identifying the isometries on a polyhedral normed linear space. In particular, we obtain refinements of the Blanco-Koldobsky-Turnšek Theorem for polyhedral normed linear spaces, including $ \ell_{\infty}^{n}, \ell_{1}^{n}. $ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On directional preservation of orthogonality and its application to isometries Manna, Jayanta Mandal, Kalidas Paul, Kallol Sain, Debmalya Functional Analysis 46B20, 46B04 We study the local preservation of Birkhoff-James orthogonality by linear operators between normed linear spaces, at a point and in a particular direction. We obtain a complete characterization of the same, which allows us to present refinements of the local preservation of orthogonality explored earlier. We also study the directional preservation of orthogonality with respect to certain special subspaces of the domain space, and apply the results towards identifying the isometries on a polyhedral normed linear space. In particular, we obtain refinements of the Blanco-Koldobsky-Turnšek Theorem for polyhedral normed linear spaces, including $ \ell_{\infty}^{n}, \ell_{1}^{n}. $ |
| title | On directional preservation of orthogonality and its application to isometries |
| topic | Functional Analysis 46B20, 46B04 |
| url | https://arxiv.org/abs/2501.02714 |