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


Authors: William B. Johnson and N. Lovasoa Randrianarivony
Journal: Proc. Amer. Math. Soc. 134 (2006), 1045-1050
MSC (2000): Primary 46B20; Secondary 51F99
DOI: https://doi.org/10.1090/S0002-9939-05-08415-7
Published electronically: November 7, 2005
MathSciNet review: 2196037
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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: https://doi.org/10.1090/S0002-9939-05-08415-7
Keywords: Coarse embedding, uniform embedding
Received by editor(s): October 7, 2004
Published electronically: 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
Article copyright: © Copyright 2005 by the authors

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