Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
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 spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.
Cite
@article{arxiv.math-ph/0404029,
title = {Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics},
author = {I. Antoniou and W. A. Majewski and Z. Suchanecki},
journal= {arXiv preprint arXiv:math-ph/0404029},
year = {2007}
}