The approximation property for spaces of holomorphic functions on infinite-dimensional spaces I

For an open subset U of a locally convex space E, let ( H( U), τ 0) denote the vector space of all holomorphic functions on U, with the compact-open topology. If E is a separable Fréchet space with the bounded approximation property, or if E is a (DFC)-space with the approximation property, we show...

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Bibliographic Details
Published in:Journal of approximation theory Vol. 126; no. 2; pp. 141 - 156
Main Authors: Dineen, Seán, Mujica, Jorge
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2004
Subjects:
(DFC)-space
Approximation property
Fréchet space
Holomorphic function
Fréchet space
Holomorphic function
Approximation property
(DFC)-space
ISSN:0021-9045, 1096-0430
Online Access:Get full text
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Summary:For an open subset U of a locally convex space E, let ( H( U), τ 0) denote the vector space of all holomorphic functions on U, with the compact-open topology. If E is a separable Fréchet space with the bounded approximation property, or if E is a (DFC)-space with the approximation property, we show that ( H( U), τ 0) has the approximation property for every open subset U of E. These theorems extend classical results of Aron and Schottenloher. As applications of these approximation theorems we characterize the spectra of certain topological algebras of holomorphic mappings with values in a Banach algebra.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2004.01.008