Given a coarse space $(X,\mathcal{E})$, one can define a $\mathrm{C}^*$-algebra $\mathrm{C}^*_u(X)$ called the uniform Roe algebra of $(X,\mathcal{E})$. It has been proved by J. \v{S}pakula and R. Willett that if the uniform Roe algebras of two uniformly locally finite metric spaces with property A are isomorphic, then the metric spaces are coarsely equivalent to each other. In this paper, we look at the problem of generalizing this result for general coarse spaces and on weakening the hypothesis of the spaces having property A.

中文翻译：

---

关于均匀局部有限粗糙空间上均匀 Roe 代数的刚性

给定一个粗糙空间 $(X,\mathcal{E})$，我们可以定义一个 $\mathrm{C}^*$-代数 $\mathrm{C}^*_u(X)$ 称为统一 Roe 代数$(X,\mathcal{E})$。J. \v{S}pakula 和 R. Willett 已经证明，如果两个具有性质 A 的一致局部有限度量空间的一致 Roe 代数是同构的，则度量空间彼此粗略等价。在本文中，我们研究了将这个结果推广到一般粗糙空间和弱化具有属性 A 的空间的假设的问题。