On some special subspaces of a Banach space, from the perspective of best coapproximation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929457031282688 |
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| author | Sohel, Shamim Ghosh, Souvik Sain, Debmalya Paul, Kallol |
| author_facet | Sohel, Shamim Ghosh, Souvik Sain, Debmalya Paul, Kallol |
| contents | We study the best coapproximation problem in Banach spaces, by using Birkhoff-James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets-Klee Property. On the other hand, we provide a sufficient condition for the strongly anti-coproximinal subspaces in a general Banach space. We also characterize the anti-coproximinal subspaces of a smooth Banach space. Further, we study these special subspaces in a finite-dimensional polyhedral Banach space and find some interesting geometric structures associated with them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some special subspaces of a Banach space, from the perspective of best coapproximation Sohel, Shamim Ghosh, Souvik Sain, Debmalya Paul, Kallol Functional Analysis 41A65, 46B20 We study the best coapproximation problem in Banach spaces, by using Birkhoff-James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obtain a necessary condition for the strongly anti-coproximinal subspaces in a reflexive Banach space whose dual space satisfies the Kadets-Klee Property. On the other hand, we provide a sufficient condition for the strongly anti-coproximinal subspaces in a general Banach space. We also characterize the anti-coproximinal subspaces of a smooth Banach space. Further, we study these special subspaces in a finite-dimensional polyhedral Banach space and find some interesting geometric structures associated with them. |
| title | On some special subspaces of a Banach space, from the perspective of best coapproximation |
| topic | Functional Analysis 41A65, 46B20 |
| url | https://arxiv.org/abs/2407.14471 |