On strong orthogonality and strictly convex normed linear spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2012
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| _version_ | 1866911998331060224 |
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| author | Paul, Kallol Sain, Debmalya Jha, Kanhaiya |
| author_facet | Paul, Kallol Sain, Debmalya Jha, Kanhaiya |
| contents | We introduce the notion of strongly orthogonal set relative to an element in the sense of Birkhoff-James in a normed linear space to find a necessary and sufficient condition for an element $ x $ of the unit sphere $ S_{X}$ to be an exposed point of the unit ball $ B_X .$ We then prove that a normed linear space is strictly convex iff for each element x of the unit sphere there exists a bounded linear operator A on X which attains its norm only at the points of the form $ λx $ with $ λ\in S_{K} $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1211_6489 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | On strong orthogonality and strictly convex normed linear spaces Paul, Kallol Sain, Debmalya Jha, Kanhaiya Functional Analysis 46B20 (Primary) 47A30 (Secondary) We introduce the notion of strongly orthogonal set relative to an element in the sense of Birkhoff-James in a normed linear space to find a necessary and sufficient condition for an element $ x $ of the unit sphere $ S_{X}$ to be an exposed point of the unit ball $ B_X .$ We then prove that a normed linear space is strictly convex iff for each element x of the unit sphere there exists a bounded linear operator A on X which attains its norm only at the points of the form $ λx $ with $ λ\in S_{K} $. |
| title | On strong orthogonality and strictly convex normed linear spaces |
| topic | Functional Analysis 46B20 (Primary) 47A30 (Secondary) |
| url | https://arxiv.org/abs/1211.6489 |