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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

References

[1] Bratteli, O., Inductive limits of finite-dimensional C*-algebras. Trans. Amer. Math. Soc. 171 (1972), 195–234.Google Scholar
[2] Effros, E. G., On the structure theory of C*-algebras: some old and new problems. In: Proc. Sympos. Pure Math. 38(1982), Part 1, 19–34.Google Scholar
[3] Futamura, H., Kataoka, N. and Kishimoto, A., Homogeneity of the pure state space for separable C*-algebras. Internat. J. Math. 12 (2001), 813–845.Google Scholar
[4] Futamura, H., Kataoka, N. and Kishimoto, A., Type III representations and automorphisms of some separable nuclear C*-algebras. Preprint.Google Scholar
[5] Haagerup, U., All nuclear C*-algebras are amenable. Invent.Math. 74 (1983), 305–319.Google Scholar
[6] Haagerup, U., The Grothendieck inequality for bilinear forms on C*-algebras. Adv. in Math. 56 (1985), 93–116.Google Scholar
[7] Kirchberg, E. and Phillips, N. C., Embedding of exact C*-algebras and continuous fields in the Cuntz algebra O2 J. Reine Angew.Math. 525 (2000), 55–94.Google Scholar
[8] Kishimoto, A., Approximately inner flows on separable C*-algebras. Preprint.Google Scholar
[9] Kishimoto, A. and Kumjian, A., The Ext class of approximately inner automorphisms, II. J. Operator Theory, to appear.Google Scholar
[10] Johnson, B. E., Kadison, R. V. and Ringrose, J. R., Cohomology of operator algebras III. Reduction to normal cohomology. Bull. Soc. Math. France 100 (1972), 73–96.Google Scholar
[11] Powers, R. T., Representations of uniformly hyperfinite algebras and their associated von Neumann rings. Ann. of Math. 86 (1967), 138–171.Google Scholar
[12] Sakai, S., C*-algebras and W*-algebras. Classics in Mathematics, Springer, 1998.Google Scholar