It is shown that the metric on the union of the sets X and Y defines a Hilbert \(C^*\)-module over the uniform Roe algebra of the space X with a fixed metric d_X. A number of examples of such Hilbert \(C^*\)-modules are described.

中文翻译：

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Hilbert $C^*$ - 与离散度量空间相关的模块

结果表明，集合X和Y的并集上的度量在具有固定度量d _X的空间X的一致 Roe 代数上定义了 Hilbert \(C^*\) -模。描述了许多此类 Hilbert \(C^*\) -模块的示例。