Approximation entropies in crossed products with an application to free shifts

Nathanial P. Brown, Marie Choda

Research output: Contribution to journalArticle

14 Scopus citations

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 languageEnglish (US)
Pages (from-to)331-346
Number of pages16
JournalPacific Journal of Mathematics
Volume198
Issue number2
DOIs
StatePublished - Apr 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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