Homogeneity of the pure state space for the separable nuclear C ∗-algebras


We prove that the pure state space is homogeneous under the action of the group of asymptotically inner automorphisms for all the separable simple nuclear C *-algebras. If simplicity is not assumed for the C *-algebras, the set of pure states whose GNS representations are faithful is homogeneous for the above action. 


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