Uniform embeddings of bounded geometry spaces into reflexive banach space

Nathanial Brown, Erik Guentner

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We show that every metric space with bounded geometry uniformly embeds into a direct sum of l p (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(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(ℕ) spaces.

Original languageEnglish (US)
Pages (from-to)2045-2050
Number of pages6
JournalProceedings of the American Mathematical Society
Volume133
Issue number7
DOIs
StatePublished - Jul 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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