Abstract
In [6] the notion of Hilbert-Stein complex spaces was introduced. The purpose of this note is to illustrate the conjecture that any Stein space whose points can be separated by bounded holomorphic functions, is Hilbert-Stein. We prove this fact for the following kinds of bounded domains of holomorphyD in Cn: 1)n=1 and π1(D) is finitely generated, 2) the group of automorphisms ofD in the compactopen topology is compact, 3)D is strongly pseudoconvex with smooth boundary andn≥2, 4)D is symmetric of type I.
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Fischer, G. Hilbert spaces of holomorphic functions on bounded domains. Manuscripta Math 3, 305–314 (1970). https://doi.org/10.1007/BF01338662
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DOI: https://doi.org/10.1007/BF01338662