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On the topological stable rank of certain transformation group $$C^*$$- algebras. (English) Zbl 0667.46045
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.
Reviewer: I.F.Putnam

##### MSC:
 46L55 Noncommutative dynamical systems
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##### References:
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