Topological entropy and AF subalgebras of graph C*-algebras
Abstract
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(E) of the canonical completely positive map E on C*(E), ht(E)=ht(E|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(E|AE) has been known recently. It is shown in this paper that ht(E|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(E|AEp)=log p are also examined.
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