Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations

Details Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations

2008-09-20

arxiv.org/abs/0809.3538v1

Mathematics

Operator Algebras

Scientific paper

For many Markov semigroups dilations in the sense of Hudson and Parthasarathy, that is a dilation which is a cocycle perturbation of a noise, have been constructed with the help of quantum stochastic calculi. In these notes we show that every Markov semigroup on the algebra of all bounded operators on a separable Hilbert space that is spatial in the sense of Arveson, admits a Hudson-Parthasarathy dilation. In a sense, the opposite is also true. The proof is based on general results on the the relation between spatial E_0-semigroups and their product systems.

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