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Uniform embeddings of bounded geometry spaces into reflexive Banach space

Authors: Nathanial Brown and Erik Guentner
Journal: Proc. Amer. Math. Soc. 133 (2005), 2045-2050
MSC (2000): Primary 46B07
Published electronically: January 21, 2005
MathSciNet review: 2137870
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Abstract: We show that every metric space with bounded geometry uniformly embeds into a direct sum of $l^p ({\mathbb N})$ spaces ($p$'s going off to infinity). In particular, every sequence of expanding graphs uniformly embeds into such a reflexive Banach space even though no such sequence uniformly embeds into a fixed $l^p ({\mathbb N})$ space. In the case of discrete groups we prove the analogue of a-$T$-menability - the existence of a metrically proper affine isometric action on a direct sum of $l^p ({\mathbb N})$ spaces.

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Additional Information

Nathanial Brown
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

Erik Guentner
Affiliation: Department of Mathematics, 2565 McCarthy Mall, University of Hawaii, Mānoa, Honolulu, Hawaii 96822-2273

Received by editor(s): September 17, 2003
Received by editor(s) in revised form: March 5, 2004
Published electronically: January 21, 2005
Additional Notes: The authors were partially supported by grants from the U.S. National Science Foundation
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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