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Traces on cores of ${C}^{\ast } $-algebras associated with self-similar maps

Published online by Cambridge University Press:  05 July 2013

TSUYOSHI KAJIWARA  and
YASUO WATATANI
TSUYOSHI KAJIWARA
Affiliation:
Department of Environmental and Mathematical Sciences, Okayama University, Tsushima, Okayama 700-8530, Japan email [email protected]
YASUO WATATANI
Affiliation:
Department of Mathematical Sciences, Kyushu University, Motooka, Fukuoka 819-0395, Japan email [email protected]
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Abstract

We completely classify the extreme tracial states on the cores of the ${C}^{\ast } $-algebras associated with self-similar maps on compact metric spaces. We present a complete list of them. The extreme tracial states are the union of the discrete type tracial states given by measures supported on the finite orbits of the branch points and a continuous type tracial state given by the Hutchinson measure on the original self-similar set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 6 , December 2014 , pp. 1964 - 1989
Copyright
© Cambridge University Press, 2013 

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