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
