### Abstract

It is shown that for two dynamical approximation entropies (one C* and one W*) the implementing inner automorphism in a crossed product A ⋊_{α} ℤ 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 script O sign_{∞} and the reduced free group C*-algebra C* (double-struck F sign_{∞}) have topological entropy zero.

Original language | English (US) |
---|---|

Pages (from-to) | 331-346 |

Number of pages | 16 |

Journal | Pacific Journal of Mathematics |

Volume | 198 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*198*(2), 331-346. https://doi.org/10.2140/pjm.2001.198.331

}

*Pacific Journal of Mathematics*, vol. 198, no. 2, pp. 331-346. https://doi.org/10.2140/pjm.2001.198.331

**Approximation entropies in crossed products with an application to free shifts.** / Brown, Nathanial; Choda, Marie.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximation entropies in crossed products with an application to free shifts

AU - Brown, Nathanial

AU - Choda, Marie

PY - 2001/1/1

Y1 - 2001/1/1

N2 - It is shown that for two dynamical approximation entropies (one C* and one W*) the implementing inner automorphism in a crossed product A ⋊α ℤ 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 script O sign∞ and the reduced free group C*-algebra C* (double-struck F sign∞) have topological entropy zero.

AB - It is shown that for two dynamical approximation entropies (one C* and one W*) the implementing inner automorphism in a crossed product A ⋊α ℤ 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 script O sign∞ and the reduced free group C*-algebra C* (double-struck F sign∞) have topological entropy zero.

UR - http://www.scopus.com/inward/record.url?scp=0001374057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001374057&partnerID=8YFLogxK

U2 - 10.2140/pjm.2001.198.331

DO - 10.2140/pjm.2001.198.331

M3 - Article

VL - 198

SP - 331

EP - 346

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -