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Proceedings of the American Mathematical Society

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Simple real rank zero algebras with locally Hausdorff spectrum

Author: Ping Wong Ng
Journal: Proc. Amer. Math. Soc. 134 (2006), 2223-2228
MSC (2000): Primary 46L35
Published electronically: March 14, 2006
MathSciNet review: 2213694
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Abstract: Let $ \mathcal{A}$ be a unital, simple, separable $ C^*$-algebra with real rank zero, stable rank one, and weakly unperforated ordered $ K_0$ group. Suppose, also, that $ \mathcal{A}$ can be locally approximated by type I algebras with Hausdorff spectrum and bounded irreducible representations (the bound being dependent on the local approximating algebra). Then $ \mathcal{A}$ is tracially approximately finite dimensional (i.e., $ \mathcal{A}$ has tracial rank zero).

Hence, $ \mathcal{A}$ is an $ AH$-algebra with bounded dimension growth and is determined by $ K$-theoretic invariants.

The above result also gives the first proof for the locally $ AH$ case.

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Additional Information

Ping Wong Ng
Affiliation: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
Address at time of publication: The Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario, Canada M5T 3J1

Received by editor(s): November 21, 2003
Received by editor(s) in revised form: June 23, 2004
Published electronically: March 14, 2006
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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