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arXiv · 2602.15525

Mazur-Ulam Theorem With Gromov-Hausdorff Distance

S. A. Bogaty·A. A. Tuzhilin
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Abstract

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.

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BibTeXRIS

S. A. Bogaty, A. A. Tuzhilin. 2026-02-17. Mazur-Ulam Theorem With Gromov-Hausdorff Distance. https://arxiv.org/abs/2602.15525

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