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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2001-45
December 2001

Perturbation theory of W*-dynamics, Liouvilleans and KMS-States


J. Derezinski, V. Jaksic, C.-A. Pillet


Given a W*-algebra $mathcal{M}$ with a W*-dynamics $tau$, we prove the existence of the perturbed W*-dynamics for a large class of unbounded perturbations. We compute its Liouvillean. If $tau$ has a $beta-KMS$ state, and the perturbation satisfies some mild assumptions related to the Golden-Thompson inequality, we prove the existence of a $beta-KMS$ state for the perturbed W*-dynamics. These results extend the well known constructions due to Araki valid for bounced perturbations.

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This paper has now been published in To appear in Reviews on Mathematical Physics