Factorization of weakly continuous holomorphic mappings

González, Manuel ; Gutiérrez, Joaqín

Studia Mathematica, Tome 119 (1996), p. 117-133 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ƒ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f = g∘S, where S is a compact operator and g a holomorphic mapping.

Détail

Publié le : 1996-01-01

Zbl 0854.46039

EUDML-ID : urn:eudml:doc:216267

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