Unbounded derivations commuting with compact group actions. \(II^*\)
type: Item
instance of: scholarly article
title: Unbounded derivations commuting with compact group actions. \(II^*\)
zbMATH Open document ID: 0547.46046
DOI: 10.1016/0022-1236(84)90006-5
author: Frederick M. Goodman
author: Antony J. Wassermann
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: Let (\({\mathcal A},G,\alpha)\) be a \(C^*\) dynamical system (with G compact) and let \(\delta\) be a closed *-derivation in \({\mathcal A}\) which commutes with \(\alpha\) (i.e. \(\alpha_ g{\mathcal D}(\delta)\subset {\mathcal D}(\delta)\) and \(\delta\circ \alpha_ g=\alpha_ g\circ\delta \) for all \(g\in G)\), such that the fixed point algebra \({\mathcal A}^ G\) is contained in \(\ker (\delta).\) The authors deal with the following question: Is it true that \(\delta\) generates a one parameter group of *-automorphisms of \({\mathcal A}?\) A first answer to this question was given by \textit{F. M. Goodman} and \textit{P. E. T. Jørgensen} in part I [Commun. Math. Phys. 82, 399-405 (1981; Zbl 0501.46061)]. In the present paper the authors show that if \({\mathcal A}\) is a separable type I \(C^*\) algebra and G is a second countable compact group, then \(\delta\) is a generator.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 3872081
zbMATH Keywords: \(C^*\) dynamical system
zbMATH Keywords: closed *-derivation
zbMATH Keywords: fixed point algebra
zbMATH Keywords: one parameter group of *-automorphisms
zbMATH Keywords: separable type I \(C^*\) algebra
zbMATH Keywords: second countable compact group
zbMATH Keywords: generator
reviewed by: Florian-Horia Vasilescu
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90006-5
OpenAlex ID: W2077719987
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description: scientific article; zbMATH DE number 3872081