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PROJECTIVE DESCRIPTION OF WEIGHTED (LF)-SPACES OF HOLOMORPHIC FUNCTIONS ON THE DISC

Published online by Cambridge University Press:  04 July 2003

Klaus D. Bierstedt  and
José Bonet
Klaus D. Bierstedt
Affiliation:
Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany ([email protected])
José Bonet
Affiliation:
Departamento de Matemática Aplicada, ETS Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain ([email protected])
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Abstract

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The topology of certain weighted inductive limits of Fréchet spaces of holomorphic functions on the unit disc can be described by means of weighted sup-seminorms in case the weights are radial and satisfy certain natural assumptions due to Lusky; in the sense of Shields and Williams the weights have to be normal. It turns out that no assumption on the (double) sequence of normal weights is necessary for the topological projective description in the case of o-growth conditions. For O-growth conditions, we give a necessary and sufficient condition (in terms of associated weights) for projective description in the case of (LB)-spaces and normal weights. This last result is related to a theorem of Mattila, Saksman and Taskinen.

AMS 2000 Mathematics subject classification: Primary 46E10. Secondary 30H05; 46A13; 46M40

Keywords

normal weightassociated weighttopological subspace
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 435 - 450
Copyright
Copyright © Edinburgh Mathematical Society 2003