Holomorphic automorphisms of continuous products of balls
type: Item
instance of: scholarly article
title: Holomorphic automorphisms of continuous products of balls
zbMATH Open document ID: 0963.32011
author: László Stachó
author: José M. Isidro
published in: Mathematische Zeitschrift
publication date: 2001-07-03T00:00:00Z
review text: Let \({\mathcal C}(\omega,E)\) denote the space of all continuous \(E\)-valued functions on \(\omega\), where \(\omega\) is a compact Hausdorff topological space and \(E\) a complex Banach space. The authors study the group of holomorphic automorphisms of continuous product domains \(D\) in \({\mathcal C} (\omega,E)\). These product domains have natural fibrations and it is of interest to understand the fiber preserving automorphisms. Denote by \(G(D)\) the identity component in the group of all holomorphic automorphisms of \(D\). If \((D_w)_{w \in\omega}\) is a family of domains in \(E\) with a mild restriction on smoothness of the boundary and some other mild condition, then for \(D=\{f\in {\mathcal C} (\omega, E):f(w)\in D_w, w\in\omega\}\) the authors show that all transformations in \(G(D)\) are fiber preserving. In the case of continuous families of balls in \(JB^*\)-triples the authors characterize the complete vector fields in the product domain reobtaining old results and also showing that others are not longer valid in the new context by providing counterexamples.
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 46L70
zbMATH DE Number: 1515374
zbMATH Keywords: continuous \(E\)-valued functions
zbMATH Keywords: group of holomorphic automorphisms
zbMATH Keywords: product domains
reviewed by: L. Barchini
MaRDI profile type: Publication
DOI: 10.1007/S002090000093
description: scientific article; zbMATH DE number 1515374