Geodesic
Ergodic properties and KMS conditions on $C^*$-symbolic dynamical systems
Documenta mathematica, Tome 16 (2011), pp. 133-175
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A C∗-symbolic dynamical system (A,ρ,Σ) consists of a unital C∗-algebra A and a finite family ρα​α∈Σ​ of endomorphisms ρα​ of A indexed by symbols α of Σ satisfying some conditions. The endomorphisms ρα​,α∈Σ yield both a subshift Λρ​ and a C∗-algebra Oρ​. We will study ergodic properties of the positive operator lambdaρ​=∑α∈Σ​ρα​ on A. We will next introduce KMS conditions for continuous linear functionals on Oρ​ under gauge action at inverse temperature taking its value in complex numbers. We will study relationships among the eigenvectors of lambdaρ​ in A∗, the continuous linear functionals on Oρ​ satisfying KMS conditions and the invariant measures on the associated one-sided shifts. We will finally present several examples of continuous linear functionals satisfying KMS conditions.
DOI : 10.4171/dm/329
Classification : 37B10, 37D35, 46L55
Mots-clés : symbolic dynamics, KMS condition, subshift, C∗-algebra, ergodic, invariant measure 
@article{10_4171_dm_329,
     author = {Kengo Matsumoto},
     title = {Ergodic properties and {KMS} conditions on $C^*$-symbolic dynamical systems},
     journal = {Documenta mathematica},
     pages = {133--175},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/329},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/329/}
}
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Kengo Matsumoto. Ergodic properties and KMS conditions on $C^*$-symbolic dynamical systems. Documenta mathematica, Tome 16 (2011), pp. 133-175. doi: 10.4171/dm/329

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