Uniform local amenability
Uniform local amenability
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DOI：
10.4171/jncg/128
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发表时间：
2012-03
影响因子：
0.9
通讯作者：
J. Brodzki;Graham A. Niblo;Ján Špakula;R. Willett;N. Wright
中科院分区：
文献类型：
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作者：
J. Brodzki;Graham A. Niblo;Ján Špakula;R. Willett;N. Wright
本文的主要结果表明，各种粗(大尺度)几何性质是密切相关的。特别地，我们证明了性质A蕴含算子范数局部化性质，从而可以有效地估计与一大类度量空间相关的算子的范数。主要工具是一种称为统一局部适应性的新属性。这个性质很容易否定，我们用它来研究一些“坏”空间。我们还推广和重新证明了Nowak在定量环境下的一个关于顺从性和渐近维度的定理。
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.