An
E
0-semigroup
acting on
is called
pure if its tail von Neumann algebra is trivial in the sense that
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 the dynamics of the state space must stabilize
as follows: for every normal state ρ of
there is convergence to equilibrium in the trace norm
A normal state ω with this property is called an
absorbing state for α.
Such E
0-semigroups must 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.
Received: 28 October 1996 / Accepted: 11
November 1996