Unbounded derivations commuting with compact group actions. \(II^*\)
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.
scientific article; zbMATH DE number 3872081