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

TL;DR

This paper proves that the pure state space of separable simple nuclear C*-algebras is homogeneous under asymptotically inner automorphisms, extending to certain pure states in non-simple cases.

Contribution

It establishes homogeneity of pure state spaces for all separable simple nuclear C*-algebras and extends results to non-simple cases with faithful GNS representations.

Findings

Pure state space is homogeneous under asymptotically inner automorphisms for all separable simple nuclear C*-algebras.

Homogeneity extends to pure states with faithful GNS representations in non-simple cases.

Provides a structural understanding of state space symmetry in nuclear C*-algebras.

Abstract

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.