Entropy and induced dynamics on state spaces

Details Entropy and induced dynamics on state spaces Entropy and induced dynamics on state spaces

2003-02-11

arxiv.org/abs/math/0302118v4

Mathematics

Operator Algebras

16 pages; some revision; to appear in GAFA

Scientific paper

We consider the topological entropy of state space and quasi-state space homeomorphisms induced from C*-algebra automorphisms. Our main result asserts that, for automorphisms of separable exact C*-algebras, zero Voiculescu-Brown entropy implies zero topological entropy on the quasi-state space (and also more generally on the entire unit ball of the dual). As an application we obtain a simple description of the topological Pinsker algebra in terms of local Voiculescu-Brown entropy.

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