2004/06/29 by Ja A Jeong, Jeong, Ja A, Gi Hyun Park +1
Mathematics · #46L05 #46L55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/0406590
12pages, submitted
arxiv created 2004/06/29 · openalex publication_date 2004/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let AE be the canonical AF subalgebra of a graph C*-algebra C*(E) associated with a locally finite directed graph E. For Brown-Voiculescu's topological entropy ht(ΦE) of the canonical completely positive map ΦE on C*(E), ht(ΦE)=ht(ΦE|AE)=hl(E)=hb(E) is known to hold for a finite graph E, where hl(E) is the loop entropy of Gurevic and hb(E) is the block entropy of Salama. For an irreducible infinite graph E, the inequality hl(E)≤ ht(ΦE|AE) has been known recently. It is shown in this paper that ht(ΦE|AE)≤ maxhb(E), hb(tE), where tE is the graph E with the direction of the edges reversed. Some irreducible infinite graphs Ep(p>1) with ht(ΦE|_AEp)=log p are also examined.