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oai:docta.ucm.es:20.500.14352/500872023-08-27T12:44:14Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Dimant, V. author Gonzalo, R. author Jaramillo Aguado, Jesús Ángel author 2009 We 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. 0022-247X 10.1112/blms/bdp077 https://hdl.handle.net/20.500.14352/50087 http://www.sciencedirect.com/science/article/pii/S0022247X08005143 http://www.sciencedirect.com/ Asymptotic structure, l(p)-estimates of sequences, and compactness of multilinear mappings