03-94 J. Derezinski, V. Jaksic, C-A. Pillet

Perturbation theory of $W^*$-dynamics, Liouvilleans and KMS-states (revised version) (523K, postscript) Mar 5, 03

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Abstract. Given a $W^*$-algebra $\fM$ 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 bounded perturbations.

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