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Let (A, G, a) be a C*-dynamical system such that G is compact, and let d be a closed *-derivation in A commuting with a. If -Aap\^(5)Cker5 and Aa is contained in the center of A, then d is the generator of a strongly continuous one-parameter group of ^-automorphis ms of A commuting with a. § 1. Introduction. We shall consider the problem of whether a closed *-derivation in a C*algebra commuting with an action of a locally compact group is the generator of a strongly continuous one-parameter group of ^-automorphis ms of the C*algebra. S. Sakai [14] first proposed this question and proved that a non-zero closed derivation in C(T) commuting with translations by elements of T is a constant multiple of differentiati on. The same result for C0CR) has been obtained by C. J. K. Batty [4] and F. Goodman [8]. F. Goodman [9] and H. Nakazato [13] generalized it to every locally compact group and compact group, respectively. In [9] the case that a locally compact group acts on its homogeneous space has also been considered. In the present paper we answer this problem in the affirmative for every ergodic action of a compact group. We shall also give some related results on non-ergodic actions of compact groups.

Derivations in {$C\sp{\ast} $}-algebras commuting with compact actions