A remark on characterizing inner product spaces via strong three-point homogeneity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914198470000640 |
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| author | Damase, Sujit Sakharam Khare, Apoorva |
| author_facet | Damase, Sujit Sakharam Khare, Apoorva |
| contents | We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$-point homogeneous metric space for any (or every) $n \geqslant 3$. The counterpart for $n=2$ is the Banach-Mazur problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08106 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A remark on characterizing inner product spaces via strong three-point homogeneity Damase, Sujit Sakharam Khare, Apoorva Functional Analysis Metric Geometry 46C15 (primary), 46B04, 46B20, 46B85 (secondary) We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$-point homogeneous metric space for any (or every) $n \geqslant 3$. The counterpart for $n=2$ is the Banach-Mazur problem. |
| title | A remark on characterizing inner product spaces via strong three-point homogeneity |
| topic | Functional Analysis Metric Geometry 46C15 (primary), 46B04, 46B20, 46B85 (secondary) |
| url | https://arxiv.org/abs/2312.08106 |