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C*-algebras of infinite real rank

Published online by Cambridge University Press:  17 April 2009

A. Chigogidze  and
V. Valov
A. Chigogidze
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada, e-mail: [email protected]
V. Valov
Affiliation:
Department of Mathematics and Computer Science, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada e-mail: [email protected]
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We introduce the notion of weakly (strongly) infinite real rank for unital C*-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C (X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C*-algebra C* (∞) of the free group on countable number of generators has strongly infinite real rank.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 487 - 496
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Alexandroff, P. and Pasynkov, B., Introduction to dimension theory„ (in Russian) (Nauka, Moscow, 1973).Google Scholar
[2]Brown, L.G. and Pedersen, G.K., ‘C *-algebra of real rank zero’, J. Functional Anal. 99 (1991), 131–149.CrossRefGoogle Scholar
[3]Chigogidze, A. and Valov, V., ‘Bounded rank of C *-algebras’, (Preprint math. OA/0109100v2, 2002).Google Scholar
[4]Murphy, G.J., C*-algebras and operator theory (Academic Press, London, 1990).Google Scholar