On the uniform Roe algebra as a Banach algebra and embeddings of ℓp uniform Roe algebras

We work on ℓp 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 ℓp spaces. Simultaneously, we obtain rigidity results for the classic uniform Roe C∗‐algebras which depend only on their Banach algebra structure.