Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces
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| Format: | Preprint |
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2018
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| _version_ | 1866914907160576000 |
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| author | Paul, Kallol Mal, Arpita Wójcik, Pawel |
| author_facet | Paul, Kallol Mal, Arpita Wójcik, Pawel |
| contents | We study left symmetric bounded linear operators in the sense of Birkhoff-James orthogonality defined between infinite dimensional Banach spaces. We prove that a bounded linear operator defined between two strictly convex Banach spaces is left symmetric if and only if it is zero operator when the domain space is reflexive and Kadets-Klee. We exhibit a non-zero left symmetric operator when the spaces are not strictly convex. We also study right symmetric bounded linear operators between infinite dimensional Banach spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1807_11166 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces Paul, Kallol Mal, Arpita Wójcik, Pawel Functional Analysis Primary 47L05, Secondary 46B20 We study left symmetric bounded linear operators in the sense of Birkhoff-James orthogonality defined between infinite dimensional Banach spaces. We prove that a bounded linear operator defined between two strictly convex Banach spaces is left symmetric if and only if it is zero operator when the domain space is reflexive and Kadets-Klee. We exhibit a non-zero left symmetric operator when the spaces are not strictly convex. We also study right symmetric bounded linear operators between infinite dimensional Banach spaces. |
| title | Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces |
| topic | Functional Analysis Primary 47L05, Secondary 46B20 |
| url | https://arxiv.org/abs/1807.11166 |