94-93 Thomas Hudetz

Topological Entropy for Appropriately Approximated C*-algebras (158K, AMS-Latex) Apr 18, 94

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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.

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