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Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space

Author(s): N. Lovasoa Randrianarivony
Journal: Proc. Amer. Math. Soc. 134 (2006), 1315-1317.
MSC (2000): Primary 46B20; Secondary 51F99
Posted: October 25, 2005
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Abstract: We show that a quasi-Banach space coarsely embeds into a Hilbert space if and only if it is isomorphic to a linear subspace of $ L_0(\mu)$ for some probability space $ (\Omega, \mathcal{B}, \mu)$.

References:

[A]
T. Aoki, Locally bounded linear topological spaces, Proc. Imp. Acad. Tokyo 18 (1942), 588-594. MR 0014182 (7:250d)

[AMM]
I. Aharoni, B. Maurey, and B. S. Mityagin, Uniform embeddings of metric spaces and of Banach spaces into Hilbert spaces, Israel J. Math. 52 (1985), no. 3, 251-265. MR 0815815 (87b:46011)

[BDK]
J. Bretagnolle, D. Dacunha Castelle, J. L. Krivine, Lois stables et espaces $ L^p$, Ann. Inst. H. Poincaré Sect. B (N. S.) 2 (1965/1966), 231-259. MR 0203757 (34:3605)

[BL]
Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Coll. Pub. 48, Amer. Math. Soc., Providence, RI, 2000. MR 1727673 (2001b:46001)

[G]
M. Gromov, Asymptotic invariants for infinite groups, Geometric Group Theory, G. A. Niblo and M. A. Roller, eds., Cambridge University Press, Cambridge, 1993. MR 1253544 (95m:20041)

[GD]
S. Guerre-Delabrière, Types et suites symétriques dans $ L^p, 1\leq p <+\infty, p\neq 2$, Israel J. Math. 53 (1986), no. 2, 191-208. MR 0845871 (87m:46047)

[JR]
W. B. Johnson and N. L. Randrianarivony, $ \ell_p$ $ (p>2)$ does not coarsely embed into a Hilbert space, Proc. Amer. Math. Soc. (to appear).

[MN]
M. Mendel, A. Naor, Euclidian quotients of finite metric spaces, Adv. Math. 189 (2004), 451-494. MR 2101227 (2005h:54031)

[Ni]
E. M. Nikišin, Resonance theorems and expansions in eigenfunctions of the Laplace operator (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 795-813, English translation: Math. USSR-Izv. 6 (1972), 788-806.

[No]
P. Nowak, Coarse embeddings of metric spaces into Banach spaces, Proc. Amer. Math. Soc. 133 (2005), 2589-2596. MR 2146202

[R]
S. Rolewicz, On a certain class of linear metric spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astrono. Phys. 5 (1957), 471-473. MR 0088682 (19:562d)

[S]
I. J. Schoenberg, Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44 (1938), 522-536. MR 1501980

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Additional Information:

N. Lovasoa Randrianarivony
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, University of Missouri-Columbia, Mathematical Sciences Building, Columbia, Missouri 65211-4100
Email: nirina@math.tamu.edu, lova@math.missouri.edu

DOI: 10.1090/S0002-9939-05-08416-9
PII: S 0002-9939(05)08416-9
Keywords: Coarse embedding, uniform embedding
Received by editor(s): November 17, 2004
Posted: October 25, 2005
Additional Notes: The author was supported in part by NSF 0200690 and Texas Advanced Research Program 010366-0033-20013.
This paper represents a portion of the author's dissertation being prepared at Texas A&M University under the direction of William B. Johnson.
Communicated by: David Preiss
Copyright of article: Copyright 2005, by the author

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