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 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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01.02.2004
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| ISSN: | 0021-9045, 1096-0430 |
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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 |
| Author_xml | – sequence: 1 givenname: Seán surname: Dineen fullname: Dineen, Seán email: sean.dineen@ucd.ie organization: Department of Mathematics, UCD, Belfield, Dublin 4, Ireland – sequence: 2 givenname: Jorge surname: Mujica fullname: Mujica, Jorge email: mujica@ime.unicamp.br organization: IMECC-UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil |
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| Cites_doi | 10.24033/bsmf.1811 10.1016/0022-247X(86)90005-3 10.4064/sm-60-3-223-238 10.1007/BF01220448 10.5802/aif.68 10.1007/BF03322663 10.1007/978-1-4684-9409-9 10.1090/S0002-9939-1969-0250067-1 10.1016/0022-247X(92)90339-F 10.1007/BF01456881 10.5802/aif.638 10.4064/sm-82-2-107-134 10.1007/BF01351314 10.1016/0022-1236(76)90026-4 10.4064/sm-40-3-239-243 |
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| Keywords | Fréchet space Holomorphic function Approximation property (DFC)-space |
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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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| SubjectTerms | (DFC)-space Approximation property Fréchet space Holomorphic function |
| Title | The approximation property for spaces of holomorphic functions on infinite-dimensional spaces I |
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