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Dynamical entropy for Bogoliubov actions of free abelian groups on the CAR-algebra

Published online by Cambridge University Press:  02 April 2001

SERGEY I. BEZUGLYI  and
VALENTIN YA. GOLODETS
SERGEY I. BEZUGLYI
Affiliation:
Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Vienna, Austria
VALENTIN YA. GOLODETS
Affiliation:
Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Vienna, Austria
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Abstract

The notion of dynamical entropy for actions of a countable free abelian group $G$ by automorphisms of $C^*$-algebras is studied. These results are applied to Bogoliubov actions of $G$ on the CAR-algebra. It is shown that the dynamical entropy of Bogoliubov actions is computed by a formula analogous to that found by Størmer and Voiculescu in the case $G={\bf Z}$, and also it is proved that the part of the action corresponding to a singular spectrum gives zero contribution to the entropy. The case of an infinite number of generators has some essential differences and requires new arguments.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 4 , August 1997 , pp. 757 - 782
Copyright
© 1997 Cambridge University Press

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