On the best coapproximation problem in $\ell_1^n$
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909293305921536 |
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| author | Sain, Debmalya Sohel, Shamim Ghosh, Souvik Paul, Kallol |
| author_facet | Sain, Debmalya Sohel, Shamim Ghosh, Souvik Paul, Kallol |
| contents | We study the best coapproximation problem in the Banach space $ \ell_1^n, $ by using Birkhoff-James orthogonality techniques. Given a subspace $\mathbb{Y}$ of $\ell_1^n$, we completely identify the elements $x$ in $\ell_1^n,$ for which best coapproximations to $x$ out of $\mathbb{Y}$ exist. The methods developed in this article are computationally effective and it allows us to present an algorithmic approach to the concerned problem. We also identify the coproximinal subspaces and co-Chebyshev subspaces of $\ell_1^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the best coapproximation problem in $\ell_1^n$ Sain, Debmalya Sohel, Shamim Ghosh, Souvik Paul, Kallol Functional Analysis Primary 46B20, Secondary 47L05 We study the best coapproximation problem in the Banach space $ \ell_1^n, $ by using Birkhoff-James orthogonality techniques. Given a subspace $\mathbb{Y}$ of $\ell_1^n$, we completely identify the elements $x$ in $\ell_1^n,$ for which best coapproximations to $x$ out of $\mathbb{Y}$ exist. The methods developed in this article are computationally effective and it allows us to present an algorithmic approach to the concerned problem. We also identify the coproximinal subspaces and co-Chebyshev subspaces of $\ell_1^n$. |
| title | On the best coapproximation problem in $\ell_1^n$ |
| topic | Functional Analysis Primary 46B20, Secondary 47L05 |
| url | https://arxiv.org/abs/2407.20102 |