On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909726912020480 |
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| author | Ghosh, Souvik Paul, Kallol Sain, Debmalya Sohel, Shamim |
| author_facet | Ghosh, Souvik Paul, Kallol Sain, Debmalya Sohel, Shamim |
| contents | This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $ C_0(K, \mathbb{X}) $, under the assumption that the unit ball of $ \mathbb{X}^* $ is the closed convex hull of its weak*-strongly exposed points. Additionally, the work includes a stability analysis of anti-coproximinal and strongly anti-coproximinal subspaces of $ \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ and the space $ \mathbb{Y} $. Beyond these, we present a general characterization of (strong) anti-coproximinal subspaces in the broader context of Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation Ghosh, Souvik Paul, Kallol Sain, Debmalya Sohel, Shamim Functional Analysis Primary 46B20, Secondary 47L05 This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $ C_0(K, \mathbb{X}) $, under the assumption that the unit ball of $ \mathbb{X}^* $ is the closed convex hull of its weak*-strongly exposed points. Additionally, the work includes a stability analysis of anti-coproximinal and strongly anti-coproximinal subspaces of $ \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ and the space $ \mathbb{Y} $. Beyond these, we present a general characterization of (strong) anti-coproximinal subspaces in the broader context of Banach spaces. |
| title | On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation |
| topic | Functional Analysis Primary 46B20, Secondary 47L05 |
| url | https://arxiv.org/abs/2508.04971 |