Comptes Rendus
no. 12
Algebra
Characterizing type I C*-algebras via entropy
[Charactérisation des algèbres de type I par l'entropie.]

Présenté par : Alain Connes

Nathanial P. Brown1
1 UC-Berkeley, Berkeley, CA 94720, USA
Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 827-829.

Soit A une C*-algèbre avec unité, séparable, nous montrons que A est de type I si et seulement si la CNT-entropie de tout automorphisme intérieur de A est nulle.

Let A be a separable unital C*-algebra. It is shown that A is type I if and only if the CNT-entropy of every inner automorphism of A is zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.06.030

Nathanial P. Brown 1

1 UC-Berkeley, Berkeley, CA 94720, USA 
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Nathanial P. Brown. Characterizing type I $ {C}^{*}$-algebras via entropy. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 827-829. doi : 10.1016/j.crma.2004.06.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.030/

[1] N.P. Brown, K. Dykema, D. Shlyakhtenko, Topological entropy of free product automorphisms, Preprint

[2] A. Connes; H. Narnhofer; W. Thirring Dynamical entropy of C*-algebras and von Neumann algebras, Commun. Math. Phys., Volume 112 (1987), pp. 691-719

[3] K. Dykema, Topological entropy for some automorphisms of reduced amalgamated free product C*-algebras, Preprint

[4] S. Neshveyev, E. Størmer, Entropy in type I algebras, Preprint

[5] V. Paulsen Completely bounded maps and dilations, Pitman Res. Notes in Math., vol. 146, Longman, 1986

[6] G. Pedersen C*-Algebras and Their Automorphism Groups, Academic Press, London, 1979

[7] E. Størmer, A survey of noncommutative dynamical entropy, Preprint

[8] D. Voiculescu Almost inductive limit automorphisms and embeddings into AF-algebras, Ergodic Theory Dynamical Systems, Volume 6 (1986), pp. 475-484

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