E_0-Semigroups for Continuous Poduct Systems: The Nonunital Case

Details E_0-Semigroups for Continuous Poduct Systems: The Nonunital Case E_0-Semigroups for Continuous Poduct Systems: The Nonunital Case

2009-01-13

arxiv.org/abs/0901.1754v1

Mathematics

Operator Algebras

Scientific paper

Let 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 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 E_0-semigroup up to stable cocycle conjugacy and continuous product systems up isomorphism. This generalizes the results for unital B to the sigma-unital case.

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