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E 0 -semigroups for continuous product systems: the nonunital case. (English) Zbl 1193.46043
Summary: Let be a σ-unital C * -algebra. We show that every strongly continuous E 0 -semigroup on the algebra of adjointable operators on a full Hilbert -module E gives rise to a full continuous product system of correspondences over . We show that every full continuous product system of correspondences over 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 to the σ-unital case.
MSC:
46L55Noncommutative dynamical systems
46L53Noncommutative probability and statistics
46L08C * -modules