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

• Published in: Ergodic theory and dynamical systems Vol. 34; no. 6; pp. 1964 - 1989
• Main Authors: KAJIWARA, TSUYOSHI, WATATANI, YASUO
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.12.2014
• Subjects: Classification; Dynamical systems; Mathematical analysis; Metric space; Orbits; Self-similarity; Unions

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...