Stochastic dilation of a quantum dynamical semigroup on a separable unital C^∗ algebra

Abstract

Given a uniformly continuous quantum dynamical semigroup on a separable unital C^∗ algebra, we construct a canonical Evans-Hudson (E-H) dilation. Such a result was already proved by Goswami and Sinha ([GS]) in the von-Neumann algebra set-up, which has been extended to the C^∗ algebraic framework in the present article. The authors make use of the coordinate-free calculus and results of [GS], but the proof of the existence of structute maps differs form that of [GS].