The quasi-orbit space of continuous $C^{\ast }$-dynamical systems

Abstract:

Let $(A,G,\alpha )$ be a separable continuous ${C^\ast }$-dynamical system. Suppose G is amenable and $\alpha$ is free on the dual  of A. Then the quasi-orbit space ${({\text {Prim}}\;A/\alpha )^ \sim }$ of the primitive ideal space Prim A of A by $\alpha$ is homeomorphic to the induced primitive ideal space which is dense in the primitive ideal space Prim ${C^\ast }(A;\alpha )$ of the ${C^\ast }$-crossed product ${C^\ast }(A;\alpha )$ of A by $\alpha$.