Uniform embeddings of bounded geometry spaces into reflexive Banach space期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Uniform embeddings of bounded geometry spaces into reflexive Banach space

Authors:	Nathanial Brown Erik Guentner

Affiliation:	Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 ; Department of Mathematics, 2565 McCarthy Mall, University of Hawaii, Manoa, Honolulu, Hawaii 96822-2273

Abstract:	We show that every metric space with bounded geometry uniformly embeds into a direct sum of $l^p ({mathbb N})$ 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 $l^p ({mathbb N})$ 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 $l^p ({mathbb N})$ spaces.

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