Dimant, V.Gonzalo, R.Jaramillo Aguado, Jesús Ángel2023-06-202023-06-2020090022-247X10.1112/blms/bdp077https://hdl.handle.net/20.500.14352/50087We relate the moduli of asymptotic uniform smoothness and convexity of a Banach space with the existence of upper and lower l(p)-estimates of sequences in the space. To this end, we introduce two properties which are related to the (m(p))-property defined by Kalton and Werner. In this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity, and compactness or weak-sequential continuity of multilinear mappings. Finally, we give some applications to the existence of analytic and asymptotically flat norms on a Banach space.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X08005143http://www.sciencedirect.com/restricted access517.98Banach spacesAsymptotic structureMultilinear operatorsPolynomialsAnálisis funcional y teoría de operadores