Another look at results of Wolff and Julia type for \(J^*\)-algebras
type: Item
instance of: scholarly article
title: Another look at results of Wolff and Julia type for \(J^*\)-algebras
zbMATH Open document ID: 0885.46045
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-12-08T00:00:00Z
review text: Let \({\mathcal L}(H, K)\) be the space of all continuous linear operators from \(H\) to \(K\), where \(H\) and \(K\) are complex Hilbert spaces. A \(J^*\)-algebra \(U\) is a closed subspace of \({\mathcal L}(H, K)\) such that \(aa^*a\in U\) for all \(a\in U\). It was shown by Harris that the open unit ball of a \(J^*\)-algebra is a bounded symmetric domain whose transitive group of automorphisms is given by the so-called linear fractional transformations. ``In this paper, some generalizations of the classical theorem of Wolff on the unit disc in the complex field are given for \(J^*\)-algebras, using techniques from the theory of circular domains in operators spaces, as developed by \textit{L. A. Harris} [Ind. Univ. Math. J. 41, No. 1, 125-147 (1992; Zbl 0760.47018)]''.
reviewed by: Antonio Fernández López
Mathematics Subject Classification ID: 46H70
zbMATH DE Number: 902510
zbMATH Keywords: space of all continuous linear operators
zbMATH Keywords: \(J^*\)-algebra
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: transitive group of automorphisms
zbMATH Keywords: linear fractional transformations
zbMATH Keywords: theorem of Wolff
Wikidata QID: Q121141614
author: Pauline Mellon
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0091
OpenAlex ID: W1972925769
DOI: 10.1006/JMAA.1996.0091
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description: scientific article; zbMATH DE number 902510