Embeddings of locally finite metric spaces into Banach spaces

Embeddings of locally finite metric spaces into Banach spaces
HTML articles powered by AMS MathViewer

by F. Baudier and G. Lancien PDF

Proc. Amer. Math. Soc. 136 (2008), 1029-1033 Request permission

We show that if $X$ is a Banach space without cotype, then every locally finite metric space embeds metrically into $X$.

References

Israel Aharoni, Every separable metric space is Lipschitz equivalent to a subset of $c^{+}_{0}$, Israel J. Math. 19 (1974), 284–291. MR 511661, DOI 10.1007/BF02757727
Nathanial Brown and Erik Guentner, Uniform embeddings of bounded geometry spaces into reflexive Banach space, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2045–2050. MR 2137870, DOI 10.1090/S0002-9939-05-07721-X
N.J. Kalton, Coarse and uniform embeddings into reflexive spaces, preprint.
G. Kasparov and G. Yu, The coarse Novikov conjecture and uniform convexity, Advances Math., to appear.
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
Bernard Maurey and Gilles Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math. 58 (1976), no. 1, 45–90 (French). MR 443015, DOI 10.4064/sm-58-1-45-90
M. Mendel, A. Naor, Metric cotype, preprint.