Completely positive quantum stochastic convolution cocycles and their dilations

Abstract

Stochastic generators of completely positive and contractive quantum stochastic convolution cocycles on a C*-hyperbialgebra are characterised. The characterisation is used to obtain dilations and stochastic forms of Stinespring decomposition for completely positive convolution cocycles on a C*-bialgebra.

20 pages; to appear in Mathematical Proceedings of the Cambridge Philosophical Society (2007)