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Journal of Convex Analysis 18 (2011), No. 2, 433--446
Copyright Heldermann Verlag 2011

Asplund Sets and Metrizability for the Polynomial Topology

Pablo Galindo
Dep. de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, 46100 Burjasot, Spain

Alejandro Miralles
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica, Edificio 8E Cubo F, Cuarta Planta, 46022 Valencia, Spain

The theme of this paper is the study of the separability of subspaces of holomorphic functions respect to the convergence over a given set and its connection with the metrizability of the polynomial topology. A notion closely related to this matter is that of Asplund set. Our discussion includes an affirmative answer to a question of Globevnik about interpolating sequences. We also consider the interplay between polynomials and Asplund sets and derive some consequences of it. Among them we obtain a characterization of Radon-Nikodym composition operators on algebras of bounded analytic functions.

Keywords: Algebras of analytic functions, Asplund set, composition operator, interpolation, polynomial topology, Radon-Nikodym property.

MSC: 46B22, 46G20; 46G10, 46J15, 47B33, 65D05

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