Distinguished preduals of spaces of holomorphic functions.

Christopher Boyd

Displaying similar documents to “Distinguished preduals of spaces of holomorphic functions.”

Holomorphic functions on strict inductive limits of Banach spaces.

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.

On τ-completeness of H(U).

J. M. Isidro (1979)

Revista Matemática Hispanoamericana

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Quasinormability of some spaces of holomorphic mappings.

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.

Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy

Seán Dineen (1975)

Bulletin de la Société Mathématique de France

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On some topological algebras of holomorphic functions.

J. M. Isidro (1979)

Revista Matemática Hispanoamericana

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Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains

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 $Π_{n = 1}^{\infty} C$ 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: ...

(LB)-structure of spaces of germs of holomorphic functions.

Nguyen Dinh Lan (2000)

Publicacions Matemàtiques

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We study the structure of spaces of germs of holomorphic functions on compact sets in Fréchet spaces for (LB) as well as for (Ω,Ω).

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen (1973)

Annales de l'institut Fourier

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This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ : (a) the compact open topology $I_{0}$ , (b) the bornological topology associated with $I_{0}$ , (c) the ported topology of Nachbin $I_{ω}$ , (d) the bornological topology associated with $I_{ω}$ ; and ...