Holomorphic retracts in \(B_H^{\infty}\)
\textit{M. Budzynska} and \textit{T. Kuczumow} [Contemporary Mathematics 364, 35--40 (2004; Zbl 1091.58005)] proved that if \(\mathcal {F}\) is a countable family of holomorphic (\(k_{ B_H^{\infty}}\)-nonexpansive) commuting self-mappings of \(B_H^{\infty}\) with a nonempty common fixed-point set, then this fixed-point set is a \(k_{ B_H^{\infty}}\)-nonexpansive retract of \(B_H^{\infty}\). In the present paper, the authors prove a general result of the same type: they show that the common fixed-point set of a commuting family of holomorphic mappings in \(B_H^{\infty}\) is either empty or a holomorphic set.
scientific article; zbMATH DE number 5017411
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