Mazur-Ulam Theorem With Gromov-Hausdorff Distance
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917277917511680 |
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| author | Bogaty, S. A. Tuzhilin, A. A. |
| author_facet | Bogaty, S. A. Tuzhilin, A. A. |
| contents | It is shown that two Banach spaces are linearly isometric if and only if the Gromov--Hausdorff distance between them is finite, in particular, zero. The proof is compilative and relies on results obtained by many researchers on the approximability of almost-surjective almost-isometries by linear surjective isometries. In the finite-dimensional case, previously obtained by I.~Mikhailov, a simpler proof under weaker assumptions is given. In the finite-dimensional case, a criterion for isometry in terms of finite (compact) subsets is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mazur-Ulam Theorem With Gromov-Hausdorff Distance Bogaty, S. A. Tuzhilin, A. A. Metric Geometry Functional Analysis 51F99 It is shown that two Banach spaces are linearly isometric if and only if the Gromov--Hausdorff distance between them is finite, in particular, zero. The proof is compilative and relies on results obtained by many researchers on the approximability of almost-surjective almost-isometries by linear surjective isometries. In the finite-dimensional case, previously obtained by I.~Mikhailov, a simpler proof under weaker assumptions is given. In the finite-dimensional case, a criterion for isometry in terms of finite (compact) subsets is also given. |
| title | Mazur-Ulam Theorem With Gromov-Hausdorff Distance |
| topic | Metric Geometry Functional Analysis 51F99 |
| url | https://arxiv.org/abs/2602.15525 |