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
galindo@uv.es
Alejandro Miralles
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica, Edificio 8E Cubo F, Cuarta Planta, 46022 Valencia, Spain
almimon@csa.upv.es
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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