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

Author: N. Lovasoa Randrianarivony
Journal: Proc. Amer. Math. Soc. 134 (2006), 1315-1317
MSC (2000): Primary 46B20; Secondary 51F99
Published electronically: October 25, 2005
MathSciNet review: 2199174
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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)$.

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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

Keywords: Coarse embedding, uniform embedding
Received by editor(s): November 17, 2004
Published electronically: 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
Article copyright: © Copyright 2005 by the author

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