Compact group actions on C∗-algebras: An application of non-commutative duality

Abstract

We first prove that for a coaction of a compact group on a C ∗-algebra A, the largest liminal (resp. postliminal) ideal of A is invariant under the coaction. As a consequence of this and an earlier characterization, by the authors, of the ideals of a crossed product algebra which are invariant under the dual coaction, we answer affirmatively a question of Landstad's and Olesen's. Specifically, we prove that if α is an action of a compact group G on a C ∗-algebra A and if the fixed-point algebra A α is liminal (resp. postliminal), then so is the crossed product algebra G × α A.