\(G\)-central states of almost periodic type on \(C^*\)-algebras (Q1174620)

Let \(G\) be a locally compact abelian group acting on a \(C^*\)-algebra \(A\). The author studies decompositions of \(G\)-invariant states on \(A\) into almost periodic states. For this he uses a notion of ``\(G\)-central states of almost periodic type''. For such states he proves spectral properties analogous to the \(G_ \Gamma\)-abelian case. Finally, necessary and sufficient conditions are established for an invariant state to be \(G\)-central of almost periodic type.