Homogeneity of the pure state space of a separable C*-algebra

2001/10/15 by Akitaka Kishimoto, A. Kishimoto, Kishimoto, A. +6 · 1 citation
Mathematics · Physics and Astronomy · #46L30 #46L40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications #math.OA #msc:46L30 #msc:46L40

paper · pdf · doi:10.48550/arxiv.math/0110152

This generalizes and replaces the paper(math.OA/0104258) with a similar title by A. Kishimoto and S. Sakai

arxiv created 2001/10/15 · openalex publication_date 2001/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algebras some 30 years ago.

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• Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem

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