Hilbert space factor of metric spaces

Alexander Lytchak; Elefterios Soultanis; Thomas Foertsch

Hilbert space factor of metric spaces

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arxiv 2503.00864 v1 pith:T3OOVZ2B submitted 2025-03-02 math.DG

Thomas Foertsch , Alexander Lytchak , Elefterios Soultanis This is my paper · ORCID

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keywords spacehilbertmetriccompletedecompositiondirectfactorfinite

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We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.

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Spaces with Riemannian curvature bounds are universally infinitesimally Hilbertian
math.MG 2025-08 unverdicted novelty 8.0 of 10

A metric space with line-splitting tangents at every point has Hilbert Sobolev spaces for every measure.

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