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Topologies on spaces of vector-valued meromorphic functions

Part of: Linear function spaces and their duals Topological linear spaces and related structures Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Enrique Jordá
Enrique Jordá
Affiliation:
Departamento de Matemática AplicadaE. Politécnica Superior de AlcoyUniversidad Politécnica de ValenciaPlaza Ferrándiz y Carbonell 2 E-03801 Alcoy (Alicante)Spain e-mail: ejorda@mat.upv.es
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Abstract

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This paper presents two natural extensions of the topology of the space of scalar meromorphic functions M(Ω) described by Grosse-Erdmann in 1995 to spaces of vector-valued meromorphic functions M(ΩE). When E is locally complete and does not contain copies of ω we compare these topologies with the topology induced by the representation M (Ω, E) ≃ M(Ω)ε E recently obtained by Bonet, Maestre and the author.

MSC classification

Secondary: 46E40: Spaces of vector- and operator-valued functions 46A03: General theory of locally convex spaces 46E05: Lattices of continuous, differentiable or analytic functions 30D30: Meromorphic functions, general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 273 - 290
Copyright
Copyright © Australian Mathematical Society 2005

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