OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Constructs separable real Banach spaces that are globally bi-Lipschitz equivalent but not linearly isomorphic, resolving the separable Lipschitz-isomorphism problem negatively. Thus even the complete metric structure up to bi-Lipschitz equivalence does not determine a separable Banach space's linear isomorphism class.
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There are separable real Banach spaces that are globally bi-Lipschitz equivalent but not linearly isomorphic. This gives a negative answer to the separable Banach-space Lipschitz-isomorphism problem.
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We construct a separable real Banach space Z that contains no linear copy of c_(0), yet is bi-Lipschitz equivalent to Z\oplus_∞ c_0. The same space contains a bi-Lipschitz image of every separable metric space.
This PDF is listed in OpenAI's formalization catalogue. See the scope and dependencies before interpreting coverage.
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