Abstract

It is shown that for two dynamical approximation entropies (one C^* and one W^*) the implementing inner automorphism in a crossed product A ⋊ _αZ has the same entropy value as the automorphism α.

Using the techniques in the proof, an example of a highly ergodic non-asymptotically abelian automorphism with topological entropy zero is also given. More specifically, it is shown that the free shifts on the Cuntz algebra O_∞ and the reduced free group C^*-algebra C_r^*(F_∞) have topological entropy zero.

Authors