Home > Research > Publications & Outputs > Quantum stochastic cocycles and completely boun...
View graph of relations

Quantum stochastic cocycles and completely bounded semigroups on operator spaces

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>2014
<mark>Journal</mark>International Mathematics Research Notices
Issue number11
Number of pages44
Pages (from-to)3096-3139
Early online date6/03/13
<mark>Original language</mark>English


An operator space analysis of quantum stochastic cocycles is undertaken. These are cocycles with respect to an ampliated CCR flow, adapted to the associated filtration of subspaces, or subalgebras. They form a noncommutative analogue of stochastic semigroups in the sense of Skorohod. One-to-one correspondences are established between classes of cocycle of interest and corresponding classes of one-parameter semigroups on associated matrix spaces. Each of these `global' semigroups may be viewed as the expectation semigroup of an associated quantum stochastic cocycle on the
corresponding matrix space. The classes of cocycle covered include completely positive contraction cocycles on an operator system, or C*-algebra; completely contractive cocycles on an operator space; and contraction operator cocycles on a Hilbert space. As indicated by Accardi and Kozyrev, the Schur-action matrix semigroup viewpoint circumvents technical (domain) limitations inherent in the theory of quantum stochastic differential equations. An infinitesimal analysis
of quantum stochastic cocycles from the present wider perspective is given in a sister paper.