Quantum stochastic cocycles and completely bounded semigroups on operator spaces
| dc.contributor.author | Lindsay, J. Martin | en |
| dc.contributor.author | Wills, Stephen J. | en |
| dc.contributor.funder | UK-India Education and Research Initiative | en |
| dc.date.accessioned | 2025-01-23T12:28:04Z | |
| dc.date.available | 2025-01-23T12:28:04Z | |
| dc.date.issued | 2013-03-06 | en |
| dc.description.abstract | 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 analog 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. Proof of the two key characterizations, namely that of completely positive contraction cocycles on a C*-algebra, and contraction cocycles on a Hilbert space, involves all of the analysis undertaken here. 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. | en |
| dc.description.sponsorship | UK-India Education and Research Initiative (Grant: Quantum Probability, Noncommutative Geometry & Quantum Information) | en |
| dc.description.status | Peer reviewed | en |
| dc.description.version | Accepted Version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Lindsay, J. M. and Wills, S.J. (2013) 'Quantum stochastic cocycles and completely bounded semigroups on operator spaces', International Mathematics Research Notices, 2014(11), pp. 3096-3139. https://doi.org/10.1093/imrn/rnt001 | en |
| dc.identifier.doi | https://doi.org/10.1093/imrn/rnt001 | en |
| dc.identifier.eissn | 1073-7928 | en |
| dc.identifier.endpage | 3139 | en |
| dc.identifier.issn | 1687-0247 | en |
| dc.identifier.issued | 11 | en |
| dc.identifier.journaltitle | International Mathematics Research Notices | en |
| dc.identifier.startpage | 3096 | en |
| dc.identifier.uri | https://hdl.handle.net/10468/16883 | |
| dc.identifier.volume | 2014 | en |
| dc.language.iso | en | en |
| dc.publisher | Oxford University Press | en |
| dc.relation.ispartof | International Mathematics Research Notices | en |
| dc.rights | © the Authors, 2013. Published by Oxford University Press. All rights reserved. | en |
| dc.subject | Operator space analysis | en |
| dc.subject | Quantum stochastic cocycles | en |
| dc.title | Quantum stochastic cocycles and completely bounded semigroups on operator spaces | en |
| dc.type | Article (peer-reviewed) | en |
| oaire.citation.issue | 11 | en |
| oaire.citation.volume | 2014 | en |
