Abstract of a paper by Baudier Florent
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.3696 or http://arXiv.org/abs/0906.3696 or by email in unzipped form by transmitting an empty message with subject line uget 0906.3696 or in gzipped form by using subject line get 0906.3696 to: math@arXiv.org.
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