Mujica, Jorge Holomorphic approximation in infinite-dimensional Riemann domains. (English) Zbl 0584.32035 Stud. Math. 82, 107-134 (1985). The main result of this paper is an infinite dimensional version of the classical Oka-Weil theorem on holomorphic approximation. Here is treated the case of pseudoconvex Riemann domains over a Fréchet space with basis. As an application it is proved that on the space of holomorphic functions on \(\Omega\), the compact-ported topology introduced by Nachbin coincides with the compact open topology, whenever \(\Omega\) is a pseudoconvex Riemann domain over a Fréchet-Schwartz space with basis. By passing to the envelope of holomorphy, this result is extended to the case of arbitrary Riemann domains over the same space. Using a result of Pełczyński, the existence of a basis in the previous results is replaced by the hypothesis of the bounded approximation property. The author obtains as particular cases some earlier results of M. Schottenloher [Ann. Inst. Fourier 26(1976), No.4, 207-237 (1976; Zbl 0309.32013)], J. A. Barroso [An. Acad. Bras. Cienc. 43, 527-546 (1971; Zbl 0246.46012)] etc. Reviewer: I.Şerb Cited in 3 ReviewsCited in 5 Documents MSC: 32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs 32T99 Pseudoconvex domains 32D10 Envelopes of holomorphy 32D05 Domains of holomorphy 32E05 Holomorphically convex complex spaces, reduction theory Keywords:Oka-Weil theorem on holomorphic approximation; pseudoconvex Riemann domains; envelope of holomorphy Citations:Zbl 0341.32012; Zbl 0309.32013; Zbl 0246.46012 PDFBibTeX XMLCite \textit{J. Mujica}, Stud. Math. 82, 107--134 (1985; Zbl 0584.32035) Full Text: DOI EuDML