Uniform Local Amenability
Metric Geometry
2012-03-29 v1 Group Theory
Operator Algebras
Abstract
The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators associated to a very large class of metric spaces can be effectively estimated. The main tool is a new property called uniform local amenability. This property is easy to negate, which we use to study some `bad' spaces. We also generalise and reprove a theorem of Nowak relating amenability and asymptotic dimension in the quantitative setting.
Cite
@article{arxiv.1203.6169,
title = {Uniform Local Amenability},
author = {Jacek Brodzki and Graham A. Niblo and Jan Spakula and Rufus Willett and Nick J. Wright},
journal= {arXiv preprint arXiv:1203.6169},
year = {2012}
}