We work on ${\ell }_p$ uniform Roe algebras associated to metric spaces, and on their mutual embedding. We generalize results of Farah and the authors to mutual embeddings of uniform Roe algebras of operators on ${\ell }_p$ spaces. Simultaneously, we obtain rigidity results for the classic uniform Roe ${\mathrm{C}}^{\ast }$‐algebras which depend only on their Banach algebra structure.

中文翻译：

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关于作为Banach代数的均匀Roe代数和ℓp均匀Roe代数的嵌入

我们致力于 ${\ell }_p$与度量空间及其相互嵌入相关的统一Roe代数。我们将Farah和作者的结果推广到算子上一致Roe代数的互嵌入${\ell }_p$空格。同时，我们获得了经典制服鱼子的刚度结果${\mathrm{C}}^{\ast }$-仅取决于其Banach代数结构的代数。