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

Open Access article
 Printed: Sep 2003
  • Akitaka Kishimoto
  • Narutaka Ozawa
  • Shôichirô Sakai
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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, 46L30 show english descriptions Automorphisms
46L40 - Automorphisms
46L30 - States

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