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On the topological stable rank of certain transformation group C*-algebras

Published online by Cambridge University Press:  19 September 2008

Ian F. Putnam
Ian F. Putnam
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5.
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Abstract

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We consider the crossed product or transformation group C*-algebras arising from actions of the group of integers on a totally disconnected compact metrizable space. Under a mild hypothesis, we give a necessary and sufficient dynamical condition for the invertibles in such a C*-algebra to be dense. We also examine the property of residual finiteness for such C*-algebras.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 197 - 207
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Blackadar, B.. K-theory for operator algebras. Math. Sci. Research Institute Publications 5, Springer-Verlag: Berlin-Heidelberg-New York, 1986.Google Scholar
[2]Cornfeld, I. P., Fomin, S. V. & Sinai, Ya. G.. Ergodic theory. Grundtehren der math. Wiss. 245, Springer-Verlag: Berlin-Heidelberg-New York, 1982.Google Scholar
[3]Effros, E. G.. Dimensions and C*-algebras. Conference Board Math. Sci. 46, American Mathematical Society: Providence, RI, 1981.Google Scholar
[4]Pedersen, G. K.. C*-algebras and their automorphism groups. London Mathematical Society Monographs 14, Academic Press: London, 1979.Google Scholar
[5]Pimsner, M. V.. Embedding some transformation group C*-algebras into AF-algebras. Ergod. Th. & Dynam. Sys. 3 (1983), 613–626.CrossRefGoogle Scholar
[6]Pimsner, M. & Voiculescu, D.. Exact sequences for K-groups and ext-groups of certain cross-product C*-algebras. J. Operator Theory 4 (1980), 93–118.Google Scholar
[7]Poon, Y. T.. AF-subalgebras of certain crossed products, Preprint.CrossRefGoogle Scholar
[8]Rieffel, M. A.. Dimensions and stable rank in the K-theory of C*-algebras. Proc. London Math. Soc. (3), 46 (1983), 301–333.CrossRefGoogle Scholar
[9]Versik, A. M.. Uniform algebraic approximation of shift and multiplication operators. Sov. Math. Dokl. 24 (1981) 97–100.Google Scholar
[10]Versik, A. M.. A theorem on periodical Markov approximation in ergodic theory. Ergodic Theory and Related Topics (Vitte, 1981), 195–206, Math. Res. 12, Akademie-Verlag: Berlin, 1981.Google Scholar
[11]Whitehead, G. W.. Elements of homotopy theory. Graduate Texts in Mathematics 61, Springer-Verlag: Berlin-Heidelberg-New York, 1978.Google Scholar
[12]Zeller-Meier, G.. Produits croises d'une C*-algebre par un group d'automorphismes. J. Math. Pures et Appl. 47 (1968), 101–239.Google Scholar