Entropy estimates for some 𝐂*-endomorphisms

Deaconu, Valentin

doi:10.1090/S0002-9939-99-05090-X

Entropy estimates for some $\mathbf {C}^\ast$-endomorphisms
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Proc. Amer. Math. Soc. 127 (1999), 3653-3658 Request permission

Abstract:

In this paper we compute the non-commutative topological entropy in the sense of Voiculescu for some endomorphisms of stationary inductive limits of circle algebras. These algebras are groupoid C*-algebras, and the endomorphisms restricted to the canonical diagonal are induced by some expansive maps, whose entropies provide a lower bound. For the upper bound, we use a result of Voiculescu, similar to the classical Kolmogorov-Sinai theorem. The same technique is used to compute the entropy of a non-commutative Markov shift.

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