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# Homogeneity of the Pure State Space of a Separable $C^*$-Algebra

Published:2003-09-01
Printed: Sep 2003
• Akitaka Kishimoto
• Narutaka Ozawa
• Shôichirô Sakai
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## 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 algbras some 30 years ago.
 MSC Classifications: 46L40 - Automorphisms 46L30 - States