On best coapproximations in subspaces of diagonal matrices
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909293299630080 |
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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 characterize the best coapproximation(s) to a given matrix $ T $ out of a given subspace $ \mathbb{Y} $ of the space of diagonal matrices $ \mathcal{D}_n $, by using Birkhoff-James orthogonality techniques and with the help of a newly introduced property, christened the $ * $-Property. We also characterize the coproximinal subspaces and the co-Chebyshev subspaces of $ \mathcal{D}_n $ in terms of the $ * $-Property. We observe that a complete characterization of the best coapproximation problem in $ \ell_{\infty}^n $ follows directly as a particular case of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On best coapproximations in subspaces of diagonal matrices Sain, Debmalya Sohel, Shamim Ghosh, Souvik Paul, Kallol Functional Analysis Primary 46B20, Secondary 47L05 We characterize the best coapproximation(s) to a given matrix $ T $ out of a given subspace $ \mathbb{Y} $ of the space of diagonal matrices $ \mathcal{D}_n $, by using Birkhoff-James orthogonality techniques and with the help of a newly introduced property, christened the $ * $-Property. We also characterize the coproximinal subspaces and the co-Chebyshev subspaces of $ \mathcal{D}_n $ in terms of the $ * $-Property. We observe that a complete characterization of the best coapproximation problem in $ \ell_{\infty}^n $ follows directly as a particular case of our approach. |
| title | On best coapproximations in subspaces of diagonal matrices |
| topic | Functional Analysis Primary 46B20, Secondary 47L05 |
| url | https://arxiv.org/abs/2407.20096 |