A note to the preceding paper by Bratteli, Goodman, and Jørgensen (Q1821318)

This paper gives the best possible improvement of a theorem of \textit{O. Bratteli, F. M. Goodman} and \textit{E. T. Jørgensen} [ibid. 61, 247-289 (1985; Zbl 0576.46050)]. Namely, adopting the notation of the above mentioned paper, we have the following Theorem. Let \(\tau\) be an action of an abelian group (compact) on a C*- algebra A satisfying the spectral condition (\(\Gamma)\), and let \(\delta\) be a *-derivation such that \[ (a)\quad D(\delta)=A_ F,\quad (b)\quad \delta (A_ F)\subseteq A_ F. \] Assuming that the dual of G is finitely generated, then the closure \({\bar \delta}\) of \(\delta\) generates a one-parameter group of *-automorphisms on A for which \(A_ F\) consists of analytic vectors.