Thomas Hudetz
Topological Entropy for Appropriately Approximated C*-algebras
(158K, AMS-Latex)
ABSTRACT. The ``classical'' topological entropy is one of the main numerical invariants
in topological dynamics on compact spaces. Here, the author's recent
development of a non-commutative generalization of topological entropy, in
the natural setting of general C*-algebras as the non-commutative
counterpart of continuous function algebras on compact spaces, is presented
in a slightly modified and improved form. This includes both a survey of
earlier results with some important corrections, and also new general results
in response to (and inspired by) a more recent counter-proposal for a
non-commutative topological entropy by K. Thomsen. Finally, some partially
new examples for the calculation of the defined topological entropy are
shown. The rather self-evident physical interpretation in the framework of
(operator-algebraic) quantum statistical mechanics and of ``chaotic'' quantum
dynamical systems is briefly touched upon.