Distinguished preduals of spaces of holomorphic functions.
Christopher Boyd (1993)
Revista Matemática de la Universidad Complutense de Madrid
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Christopher Boyd (1993)
Revista Matemática de la Universidad Complutense de Madrid
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Seán Dineen, Luiza A. Moraes (1992)
Revista Matemática de la Universidad Complutense de Madrid
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In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Seán Dineen (1975)
Bulletin de la Société Mathématique de France
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José M. Isidro (1990)
Revista Matemática de la Universidad Complutense de Madrid
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A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.
J. M. Isidro (1979)
Revista Matemática Hispanoamericana
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Sean Dineen (1973)
Annales de l'institut Fourier
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In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following: ...
Leopoldo Nachbin (1986)
Extracta Mathematicae
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García, Domingo (1988)
Portugaliae mathematica
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