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Characterizations of topological dynamical systems whose transformation group C*-algebras are antiliminal and of type 1

Published online by Cambridge University Press:  19 September 2008

Nobuo Aoki  and
Jun Tomiyama
Nobuo Aoki
Affiliation:
Department of Mathematics, Faculty of Science, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-03, Japan
Jun Tomiyama
Affiliation:
Department of Mathematics, Faculty of Science, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-03, Japan
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Abstract

For a topological dynamical system Σ = (X, σ) where X is a compact metric space with a single homeomorphism σ, we determine the largest postliminal ideal of the transformation group C*-algebra A(Σ) as the intersection of all kernels of irreducible representations of A(Σ) induced from those recurrent points which are not periodic. The result implies characterizations of topological dynamical systems whose transformation group C*-algebras are anti-liminal and post-liminal, that is, of type 1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 1 - 5
Copyright
Copyright © Cambridge University Press 1993

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References

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