2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158505We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.20 pages, to appear in Israel Journal of MathematicsFunctional Analysis46B20, 47L10 (Primary); 16E40 (Secondary)text