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

Published online by Cambridge University Press:  20 November 2018

Akitaka Kishimoto ,
Narutaka Ozawa  and
Shôichirô Sakai
Akitaka Kishimoto
Affiliation:
Department of Mathematics Hokkaido University Sapporo Japan 060-0810
Narutaka Ozawa
Affiliation:
Department of Mathematical Sciences University of Tokyo Tokyo Japan 153-8914
Shôichirô Sakai
Affiliation:
5-1-6-205 Odawara Aoba-ku Sendai Japan 980-0003
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Abstract

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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 $\text{UHF}$ algbras some 30 years ago.

Keywords

46L4046L30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 365 - 372
Copyright
Copyright © Canadian Mathematical Society 2003

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