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Embeddings of locally finite metric spaces into Banach spaces
Author(s):
F.
Baudier;
G.
Lancien
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1029-1033.
MSC (2000):
Primary 46B25;
Secondary 51F99
Posted:
November 28, 2007
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Abstract:
We show that if  is a Banach space without cotype, then every locally finite metric space embeds metrically into  .
References:
-
- 1.
- I. Aharoni, Every separable metric space is Lipschitz equivalent to a subset of
 , Israel J. Math., 19 1974, 284-291. MR 0511661 (58:23471a) - 2.
- N. Brown and E. Guentner, Uniform embeddings of bounded geometry spaces into reflexive Banach spaces, Proc. Amer. Math. Soc., 133(7) 2005, 2045-2050. MR 2137870 (2006b:57044)
- 3.
- N.J. Kalton, Coarse and uniform embeddings into reflexive spaces, preprint.
- 4.
- G. Kasparov and G. Yu, The coarse Novikov conjecture and uniform convexity, Advances Math., to appear.
- 5.
- J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I, Springer, Berlin 1977. MR 0500056 (58:17766)
- 6.
- B. Maurey, G. Pisier, Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach, Studia Math., 58(1) 1976, 45-90. MR 0443015 (56:1388)
- 7.
- M. Mendel, A. Naor, Metric cotype, preprint.
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Additional Information:
F.
Baudier
Affiliation:
Laboratoire de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
Email:
florent.baudier@univ-fcomte.fr
G.
Lancien
Affiliation:
Laboratoire de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
Email:
gilles.lancien@univ-fcomte.fr
DOI:
10.1090/S0002-9939-07-09109-5
PII:
S 0002-9939(07)09109-5
Received by editor(s):
October 4, 2006
Received by editor(s) in revised form:
January 10, 2007
Posted:
November 28, 2007
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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