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

DOI:
https://doi.org/10.1090/S0002-9939-05-07721-X

Published electronically:
January 21, 2005

MathSciNet review:
2137870

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every metric space with bounded geometry uniformly embeds into a direct sum of spaces ('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 space. In the case of discrete groups we prove the analogue of a--menability - the existence of a metrically proper affine isometric action on a direct sum of spaces.

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Additional Information

**Nathanial Brown**

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

Email:
nbrown@math.psu.edu

**Erik Guentner**

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

Email:
erik@math.hawaii.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-07721-X

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.