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Asymptotic structure, l(p)-estimates of sequences, and compactness of multilinear mappings

Dimant, V. and Gonzalo, R. and Jaramillo Aguado, Jesús Ángel (2009) Asymptotic structure, l(p)-estimates of sequences, and compactness of multilinear mappings. Journal of Mathematical Analysis and Applications, 350 (2). pp. 680-693. ISSN 0022-247X

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Banach spaces; Asymptotic structure; Multilinear operators; Polynomials
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16252
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