Uniform embeddings of bounded geometry spaces into reflexive Banach space

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 i...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-07, Vol.133 (7), p.2045-2050
Main Authors: Nathanial Brown, Guentner, Erik
Format: Article
Language:English
Subjects:
Banach space
Embeddings
Exact sciences and technology
Functional analysis
Geometry
Hilbert spaces
Mathematical analysis
Mathematical theorems
Mathematics
Numbers
Preprints
Real numbers
Sciences and techniques of general use
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07721-X