The bounded approximation property for spaces of holomorphic mappings on infinite dimensional spaces

We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Fréchet–Schwartz space or (DFM )‐space E , then the space ℋ︁(U ) of holomorphic mappings on U , with the compact‐open topology, has the bounded approximation property if...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 279; no. 7; pp. 705 - 715
Main Author Çalışkan, Erhan
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag 01.05.2006
WILEY‐VCH Verlag
Subjects
Approximation property
bounded approximation property
germs of holomorphic functions
holomorphic mappings
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Summary:We study the bounded approximation property for spaces of holomorphic functions. We show that if U is a balanced open subset of a Fréchet–Schwartz space or (DFM )‐space E , then the space ℋ︁(U ) of holomorphic mappings on U , with the compact‐open topology, has the bounded approximation property if and only if E has the bounded approximation property. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bibliography:ArticleID:MANA200310387
istex:F795E90E79DBE1F5F2A6808F6AACBF3502217ED0
ark:/67375/WNG-W6Q93LX9-S
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200310387