We explain how the GNS-product system of a Markov semigroup can be used to dilate that Markov semigroup. If (and only if) the Markov semigroup is spatial, the dilation is a cocycle perturbation of a noise. We explain that every noise is a monotone noise, and that every monotone noise can be \blown up" to a free noise.

Dilations of Markov Semigroups with the Help of Product Systems

SKEIDE, Michael
2011-01-01

Abstract

We explain how the GNS-product system of a Markov semigroup can be used to dilate that Markov semigroup. If (and only if) the Markov semigroup is spatial, the dilation is a cocycle perturbation of a noise. We explain that every noise is a monotone noise, and that every monotone noise can be \blown up" to a free noise.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11695/18114
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