Convergence of local charges and continuity properties of \(W^*\)- inclusions (Q1110780)

This paper is concerned with the action of compact groups of automorphisms, G, on a unital \(C^*\)-algebra A. For G being abelian, one can define \[ A^{\alpha}(\gamma):=\{x\in A:\alpha_ g(x)=(g,\gamma)x,\quad g\in G,\quad \gamma \in \hat G\}, \] whereas in the non-abelian case one takes instead the subspace \[ \{x\in A\times M_{nd}:(\alpha_ g\times 1)x=x(1\times \gamma_ g),\quad g\in G\}, \] d\(=Dim d(\gamma)\) of \(\gamma_ g\), \(M_{nd}=the\) complex \(n\times d\)- matrices. (Extended action.) Various theorems are proved, the proofs being mostly quite difficult and technical.