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Topological entropy for the canonical completely positive maps on graph C*-Algebras

Published online by Cambridge University Press:  17 April 2009

Ja A. Jeong  and
Gi Hyun Park
Ja A. Jeong
Affiliation:
Mathematical Sciences Division, BK21, Seoul National University, Seoul, 151–742, Korea, e-mail: Jajeong@math.snu.ac.kr
Gi Hyun Park
Affiliation:
Department of Mathematics, Hanshin University, Osan, 447–791, Korea, e-mail: ghpark@hanshin.ac.kr
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Let C*(E) = C*(se, pv) be the graph C*-algebra of a directed graph E = (E0, E1) with the vertices E0 and the edges E1. We prove that if E is a finite graph (possibly with sinks) and φE: C*(E) → C*(E) is the canonical completely positive map defined by then Voiculescu's topological entropy ht(φE) of φE is log r(AE), where r(AE) is the spectral radius of the edge matrix AE of E. This extends the same result known for finite graphs with no sinks. We also consider the map φE when E is a locally finite irreducible infinite graph and prove that , where the supremum is taken over the set of all finite subgraphs of E.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 101 - 116
Copyright
Copyright © Australian Mathematical Society 2004

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