Holomorphic retracts in \(B_H^{\infty}\)
type: Item
instance of: scholarly article
title: Holomorphic retracts in \(B_H^{\infty}\)
zbMATH Open document ID: 1091.37010
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-04-06T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 46T25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 58B12
zbMATH DE Number: 5017411
zbMATH Keywords: fixed points
zbMATH Keywords: holomorphic mappings
zbMATH Keywords: nonexpansive mappings
zbMATH Keywords: retracts
author: Monika Budzyńska
author: M. A. Khamsi
reviewed by: Srinivasa Swaminathan
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.08.089
OpenAlex ID: W1620740841
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DOI: 10.1016/J.JMAA.2005.08.089
description: scientific article; zbMATH DE number 5017411