Traces on cores of C∗-algebras associated with self-similar maps

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We completely classify the extreme tracial states on the cores of the C∗-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.

Original languageEnglish
Pages (from-to)1964-1989
Number of pages26
JournalErgodic Theory and Dynamical Systems
Volume34
Issue number6
DOIs
Publication statusPublished - Apr 3 2013

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Algebra
C*-algebra
Orbits
Extremes
Trace
Self-similar Set
Branch Point
Compact Metric Space
Union
Orbit
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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Traces on cores of C∗-algebras associated with self-similar maps. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Ergodic Theory and Dynamical Systems, Vol. 34, No. 6, 03.04.2013, p. 1964-1989.

Research output: Contribution to journalArticle

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