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Homogeneity of the Pure State Space of a Separable $C^*$-Algebra |
Canad. Math. Bull. 46(2003), 365-372
Published:2003-09-01
Printed: Sep 2003
Printed: Sep 2003
- Akitaka Kishimoto
- Narutaka Ozawa
- Shôichirô Sakai
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 |