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

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 th...

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Published inErgodic theory and dynamical systems Vol. 34; no. 6; pp. 1964 - 1989
Main Authors KAJIWARA, TSUYOSHI, WATATANI, YASUO
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2014
Subjects
Classification
Dynamical systems
Mathematical analysis
Metric space
Orbits
Self-similarity
Unions
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2013.26