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 ${\mathrm{C}}_{\mathrm{u}}^{\ast }(X)$. We prove that exactness and local reflexivity of ${\mathrm{C}}_{\mathrm{u}}^{\ast }(X)$ also characterize property A of $X$.

中文翻译：

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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 ${\mathrm{C}}_{\mathrm{ü}}^{\ast }（X）$。我们证明了的精确性和局部反射性${\mathrm{C}}_{\mathrm{ü}}^{\ast }（X）$ 还表征了 $X$。