%0 Journal Article
%A Dimant, V.
%A Gonzalo, R.
%A Jaramillo Aguado, Jesús Ángel
%T Asymptotic structure, l(p)-estimates of sequences, and compactness of multilinear mappings
%D 2009
%@ 0022-247X
%U https://hdl.handle.net/20.500.14352/50087
%X 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.
%~