论文标题
均等预测系列的运营商规范本地化属性
Operator norm localization property for equi-approximable families of projections
论文作者
论文摘要
最近解决了均匀的ROE代数的刚性问题。在发现其溶液之前，在某些技术几何条件的假设下存在正溶液。在本文中，我们介绍了操作员规范本地化属性（ONL）的较弱版本，这些属性是表征这些技术几何条件的。我们使用它来为不可过度的粗略空间获得新的刚性结果。作为一种应用，我们为白色和威利特关于统一的Roe代数的Cartan子代数的问题提供了一个新的部分答案。我们还研究均匀的ROE代数之间的嵌入。
The rigidity problem for uniform Roe algebras was recently positively solved. Before its solution was found, there were positive solutions under the assumption of certain technical geometric conditions. In this paper, we introduce weaker versions of the operator norm localization property (ONL) which turn out to characterize those technical geometric conditions. We use this to obtain new rigidity results for nonmetrizable coarse spaces. As an application, we provide a novel partial answer to a question of White and Willett about Cartan subalgebras of uniform Roe algebras. We also study embeddings between uniform Roe algebras.
