  We work on $\ell_p$ uniform Roe algebras associated to metric spaces, and on
their mutual embedding. We generalize results of I. 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
$\mathrm{C}^*$-algebras which depend only on their Banach algebra structure.
