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

2001/04/27 by Akitaka Kishimoto, Kishimoto, A., Shôichirô Sakai +1
Mathematics · #46L30 #46L40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0104258

openalex publication_date 2001/04/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Topological Entropy of Free Product Automorphisms

Related

• Homegeneity of the pure state space for separable C*-algebras
• Homogeneity of the pure state space of a separable C*-algebra
• Uniform property Gamma
• Nuclear dimension and Z-stability of pure C*-algebras
• Nuclear dimension and classification of C*-algebras associated to Smale spaces