Embeddings of proper metric spaces into Banach spaces

Details Embeddings of proper metric spaces into Banach spaces Embeddings of proper metric spaces into Banach spaces

2009-06-19

arxiv.org/abs/0906.3696v1

Mathematics

Functional Analysis

16 pages

Scientific paper

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any $\mathcal{L}_p$-space into any Banach space $X$ containing the $\ell_p^n$'s. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds.

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