Topological entropy for the canonical completely positive maps on graph C-Algebras
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...
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| Veröffentlicht in: | Bulletin of the Australian Mathematical Society 2004-08, Vol.70 (1), p.101-116 |
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| creator | Jeong, Ja A. Park, Gi Hyun |
| description | 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. |
| doi_str_mv | 10.1017/S0004972700035851 |
| format | Article |
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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.</description><identifier>ISSN: 0004-9727</identifier><identifier>EISSN: 1755-1633</identifier><identifier>DOI: 10.1017/S0004972700035851</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Apexes ; Entropy ; Graph theory ; Topology</subject><ispartof>Bulletin of the Australian Mathematical Society, 2004-08, Vol.70 (1), p.101-116</ispartof><rights>Copyright © Australian Mathematical Society 2004</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-d089f3b95f01d18fa6c3f6822ed6c3cd3993d3128a44c405d853840f51fd34733</citedby><cites>FETCH-LOGICAL-c396t-d089f3b95f01d18fa6c3f6822ed6c3cd3993d3128a44c405d853840f51fd34733</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0004972700035851/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,778,782,27911,27912,55615</link.rule.ids></links><search><creatorcontrib>Jeong, Ja A.</creatorcontrib><creatorcontrib>Park, Gi Hyun</creatorcontrib><title>Topological entropy for the canonical completely positive maps on graph C-Algebras</title><title>Bulletin of the Australian Mathematical Society</title><addtitle>Bull. Austral. Math. Soc</addtitle><description>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. 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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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0004972700035851</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge University Press Journals Complete |
| subjects | Apexes Entropy Graph theory Topology |
| title | Topological entropy for the canonical completely positive maps on graph C-Algebras |
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