Abstract
We show that a product subsystem of a time ordered system (that is, a product system of time ordered Fock modules), even one of type I, need not be isomorphic to a time ordered product system. In this way, we answer an open problem in the classification of CP-semigroups by product systems. We define spatial strongly continuous CP-semigroups on a unital C ∗ C^* -algebra and characterize them as those CP-semigroups that have a Christensen-Evans generator.
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