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Finite‐dimensional approximation properties for uniform Roe algebras
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2020-04-08 , DOI: 10.1112/jlms.12330
Hiroki Sako 1
Affiliation  

We study property A for metric spaces X with bounded geometry introduced by Guoliang Yu. Property A is an amenability‐type condition, which is less restrictive than amenability for groups. The property has a connection with finite‐dimensional approximation properties in the theory of operator algebras. It has been already known that property A of a metric space X with bounded geometry is equivalent to nuclearity of the uniform Roe algebra C u ( X ) . We prove that exactness and local reflexivity of C u ( X ) also characterize property A of X .

中文翻译:

均匀Roe代数的有限维逼近性质

我们研究度量空间的属性A X 由俞国良介绍的有限几何 属性A是一个可满足性类型的条件,它的限制比对组的可满足性要少。该性质与算子代数理论中的有限维逼近性质有关。已知度量空间的属性A X 有界几何等效于均匀Roe代数的核 C ü X 。我们证明了的精确性和局部反射性 C ü X 还表征了 X
更新日期:2020-04-08
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