Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics

Details Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics

2004-04-10

arxiv.org/abs/math-ph/0404029v1

Open Sys.$&$ Information Dyn, vol. 9, 301-313, 2002

Physics

Mathematical Physics

Scientific paper

We extend the concept of implementability of semigroups of evolution
operators associated with dynamical systems to quantum case. We show that such
an extension can be properly formulated in terms of Jordan morphisms and
isometries on non-commutative $L^p$ spaces. We focus our attention on a
non-commutative analog of the Banach-Lamperti theorem.

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