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Results tagged with hilbert-spaces
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user 61536
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
16
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A reference to a characterization of metric spaces admitting an isometric embedding into a H...
I am looking for a reference to the bipartite version of the Schoenberg's criterion of embeddability into a Hilbert space. The Schoenberg criterion is formulated as Proposition 8.5(ii) of the book "G …
- 41.8k
10
votes
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answers
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A characterization of metric spaces admitting a bi-Lipschitz embedding into a Hilbert space?
Theorem (??) derived in this MO-post from Schoenberg's theorem yeilds a "bipartite" characterization of metric spaces that admit an isometric embedding into a Hilbert space. This Theorem (??) implies …
CommunityBot
- 1
4
votes
2
answers
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Compact images of nowhere dense closed convex sets in a Hilbert space
Let $B=-B$ be a nowhere dense bounded closed convex set in the Hilbert space $\ell_2$ such that the linear hull of $B$ is dense in $\ell_2$.
Question. Is there a non-compact linear bounded operato …
- 31.5k
8
votes
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answer
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Equi-Hölder embeddings of compact metric spaces of finite packing dimension into $\ell_2$
Problem. Does a compact metric space of finite packing dimension admit an equi-Hölder embedding into a Hilbert space?
A map $f:X\to Y$ between metric spaces $(X,d_X)$, $(Y,d_Y)$ is called equi-Hölder …
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