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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Vydané v:Journal of approximation theory Ročník 126; číslo 2; s. 141 - 156
Hlavní autori: Dineen, Seán, Mujica, Jorge
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.02.2004
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Abstract 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.
AbstractList 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.
Author Mujica, Jorge
Dineen, Seán
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Issue 2
Keywords Fréchet space
Holomorphic function
Approximation property
(DFC)-space
Language English
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Snippet 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....
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StartPage 141
SubjectTerms (DFC)-space
Approximation property
Fréchet space
Holomorphic function
Title The approximation property for spaces of holomorphic functions on infinite-dimensional spaces I
URI https://dx.doi.org/10.1016/j.jat.2004.01.008
Volume 126
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