E0–Semigroups for Continuous Poduct Systems: The Nonunital Case
نویسنده
چکیده
Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countable 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 E0–semigroup up to stable cocycle conjugacy and continuous product systems up isomorphism. This generalizes the results for unital B to the σ–unital case.
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