Pure E_0-semigroups and absorbing states

Abstract

An E_0-semigroup acting on B(H) is called pure if the intersection of the ranges ${\alpha }_t(B(H))$, $t>0$, is the algebra of scalars. We determine all pure E_0-semigroups which have a weakly continuous invariant state $\omega$ and which are minimal in an appropriate sense. In such cases, for every normal state $\rho$ there is convergence to equilibrium in the trace norm ${\lim }_{t\to \infty }\Vert \rho \circ {\alpha }_t-\omega \Vert =0.$ A normal state $\omega$ 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.

27 pp. AMS-TeX 2.0

References in corpus (2)

• Endomorphisms of B(H)
• Noncommutative flows I: dynamical invariants

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