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Lipschitz equivalent Banach spaces need not be linearly isomorphic

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.

Manuscripts in this family · 2

Lipschitz Equivalent Separable Banach Spaces Need Not Be Linearly Isomorphic

Sep 24, 2026·paper.pdfLean

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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Bi-Lipschitz Absorption of c0 Without a Linear Copy of c0

Sep 26, 2026·paper.pdfLean

We construct a separable real Banach space Z that contains no linear copy of c

_{0}

, yet is bi-Lipschitz equivalent to

Z\oplus_\infty c_0

. The same space contains a bi-Lipschitz image of every separable metric space.

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