Geodesic
Factorization of weakly continuous holomorphic mappings
Studia Mathematica, Tome 118 (1996) no. 2, pp. 117-133

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-118-2-117-133
Keywords: weakly continuous holomorphic mapping, factorization of holomorphic mappings, polynomial, weakly continuous multilinear mapping

Manuel González 1 ;  1

1 
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Manuel González;  . Factorization of weakly continuous holomorphic mappings. Studia Mathematica, Tome 118 (1996) no. 2, pp. 117-133. doi: 10.4064/sm-118-2-117-133

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