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

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