A projective limit representation of (DFC)-spaces with the approximation property (Q1083647)

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 \(\Omega\).