%0 Journal Article
%T Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations
%A Michael Skeide
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0809.3538v1