Subsystems of Fock need not be Fock: Spatial CP-semigroups

Bhat, B.; Liebscher, Volkmar; Skeide, Michael

doi:10.1090/S0002-9939-10-10260-3

Subsystems of Fock need not be Fock: Spatial CP-semigroups
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by B. V. Rajarama Bhat, Volkmar Liebscher and Michael Skeide PDF

Proc. Amer. Math. Soc. 138 (2010), 2443-2456 Request permission

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 $C^*$-algebra and characterize them as those CP-semigroups that have a Christensen-Evans generator.

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