@article{1193.46043,
author="Skeide, Michael",
title="{$E_0$-semigroups for continuous product systems: the nonunital case.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="3",
number="2",
pages="16-27",
year="2009",
abstract="{Summary: Let $\cal B$ be a $\sigma$-unital $C^*$-algebra. We show
    that every strongly continuous $E_0$-semigroup on the algebra of adjointable
    operators on a full Hilbert $\cal B$-module $E$ gives rise to a full
    continuous product system of correspondences over $\cal B$. We show that
    every full continuous product system of correspondences over $\cal B$ arises
    in that way. If the product system is countably generated, then $E$ can be
    chosen countably generated, and if $E$ is countably generated, then so is
    the product system. We show that under these countability hypotheses there
    is a one-to-one correspondence between $E_0$-semigroups up to stable cocycle
    conjugacy and continuous product systems up to isomorphism. This generalizes
    the results for unital $\cal B$ to the $\sigma $-unital case.}",
keywords="{quantum probability; quantum dynamics; product system; Hilbert
    module}",
classmath="{*46L55 (Noncommutative dynamical systems)
46L53 (Noncommutative probability and statistics)
46L08 (C*-modules)
}",
}