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- W2030197547 abstract "Let C ∗ ( E ) be the C ∗ -algebra associated with a locally finite directed graph E and A E be the AF core of C ∗ ( E ) . For the topological entropy ht ( Φ E ) (in the sense of Brown–Voiculescu) of the canonical completely positive map Φ E on the graph C ∗ -algebra, it is known that if E is finite ht ( Φ E ) = ht ( Φ E | A E ) = h b ( E ) = h l ( E ) , where h b ( E ) (respectively, h l ( E ) ) is the block (respectively, the loop) entropy of E . In case E is irreducible and infinite, h l ( E ) ⩽ ht ( Φ E | A E ) ⩽ h b ( E t ) is known recently, where E t is the graph E with the edges directed reversely. Then by monotonicity of entropy, h l ( E ) ⩽ ht ( Φ E ) is clear. In this paper we show that ht ( Φ E ) ⩽ h b ( E t ) holds for locally finite infinite graphs E . The AF core A E is known to be stably isomorphic to the graph C ∗ -algebra C ∗ ( E × c Z ) of certain skew product E × c Z and we also show that ht ( Φ E × c Z ) = ht ( Φ E | A E ) . Examples E p ( p > 1 ) of irreducible graphs with ht ( Φ E p ) = log p are discussed." @default.
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- W2030197547 date "2009-06-01" @default.
- W2030197547 modified "2023-09-28" @default.
- W2030197547 title "Topological entropy and the AF core of a graph <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>C</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math>-algebra" @default.
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- W2030197547 doi "https://doi.org/10.1016/j.jmaa.2009.01.005" @default.
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