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arXiv · funct-an/9705004

Pure E_0-semigroups and absorbing states

William Arveson
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Abstract

An E_0-semigroup acting on B(H) is called pure if the intersection of the ranges $α_t(B(H))$, $t>0$, is the algebra of scalars. We determine all pure E_0-semigroups which have a weakly continuous invariant state $ω$ and which are minimal in an appropriate sense. In such cases, for every normal state $ρ$ there is convergence to equilibrium in the trace norm $\lim_{t\to\infty}\| ρ\circα_t - ω\| = 0.$ A normal state $ω$ with this property is called an absorbing state. Such E_0-semigroups mest be cocycle perturbations of CAR/CCR flows, and we develop systematic methods for constructing those perturbations which have absorbing states with prescribed finite eigenvalue lists.

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William Arveson. 1997-05-25. Pure E_0-semigroups and absorbing states. https://doi.org/10.1007/s002200050128

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