Subsystems of Fock Need Not Be Fock: Spatial CP-Semigroups

Details Subsystems of Fock Need Not Be Fock: Spatial CP-Semigroups Subsystems of Fock Need Not Be Fock: Spatial CP-Semigroups

2008-04-14

arxiv.org/abs/0804.2169v2

Mathematics

Operator Algebras

Revised and enlarged version, to appear in Proc. Amer. Math. Soc

Scientific paper

We show that a product subsystem of a time ordered system (that is, a product system of time ordered Fock modules), though type I, need not be isomorphic to a time ordered product system. In that 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*-algebra and characterize them as those that have a Christensen-Evans generator.

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