This is an announcement for the paper "Embeddings of proper metric spaces into Banach spaces" by Baudier Florent.

Abstract: 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.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 46B20; 51F99

Remarks: 16 pages

The source file(s), proper.tex: 34599 bytes, is(are) stored in gzipped form as 0906.3696.gz with size 10kb. The corresponding postcript file has gzipped size 91kb.

Submitted from: florent.baudier@univ-fcomte.fr

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