Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Completely positive quantum stochastic convolution cocycles and their dilations

ADAM G. SKALSKIa1 p1

a1 Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF. e-mail: a.skalski@lancaster.ac.uk

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.

(Received April 04 2006)

(Revised August 25 2006)

Correspondence:

p1 Permanent address: Department of Mathematics, University of Łódź, ul. Banacha 22, 90-238 Łódź, Poland.