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$ \ell_p$ ($ p>2$) does not coarsely embed into a Hilbert space

Author(s): William B. Johnson; N. Lovasoa Randrianarivony
Journal: Proc. Amer. Math. Soc. 134 (2006), 1045-1050.
MSC (2000): Primary 46B20; Secondary 51F99
Posted: November 7, 2005
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Abstract: We show that a Banach space with a normalized symmetric basis behaving like that of $ \ell_p$ ($ p>2$) cannot coarsely embed into a Hilbert space.

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Additional Information:

William B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

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, Missouri 65211-4100
Email: nirina@math.tamu.edu, lova@math.missouri.edu

DOI: 10.1090/S0002-9939-05-08415-7
PII: S 0002-9939(05)08415-7
Keywords: Coarse embedding, uniform embedding
Received by editor(s): October 7, 2004
Posted: November 7, 2005
Additional Notes: Both authors were supported in part by NSF 0200690 and Texas Advanced Research Program 010366-0033-20013.
This paper represents a portion of the second author's dissertation being prepared at Texas A&M University under the direction of the first author.
Communicated by: David Preiss
Copyright of article: Copyright 2005, by the authors

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