A projective limit representation of (DFC)-spaces with the approximation property
type: Item
instance of: scholarly article
title: A projective limit representation of (DFC)-spaces with the approximation property
zbMATH Open document ID: 0604.46001
DOI: 10.1016/0022-247X(86)90005-3
author: Mary Lilian Lourenço
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: We show that each (DFC)-space with the approximation property is a precompact projective limit of a family of normed spaces with monotone Schauder basis. As an application of this representation we obtain the following result on holomorphic approximation on (DFC)-spaces: LET \(\Omega\) be a pseudoconvex open set in a (DFC)-space E with the approximation property. Let K be a compact subset of \(\Omega\) such that \(\hat K_{p_ s(\Omega)}=K\). Then each function which is holomorphic on a neighbourhood of K can be uniformly approximated on a suitable neighbourhood of K by functions which are holomorphic on all of \(\Omega\).
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46M40
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 3975608
zbMATH Keywords: each (DFC)-space with the approximation property is a precompact projective limit of a family of normed spaces with monotone Schauder basis
zbMATH Keywords: holomorphic approximation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3975608