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Quantum stochastic cocycles and completely bounded semigroups on operator spaces

Lindsay, J. Martin and Wills, Stephen J. (2014) Quantum stochastic cocycles and completely bounded semigroups on operator spaces. International Mathematics Research Notices, 2014 (11). pp. 3096-3139. ISSN 1073-7928

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    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 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.

    Item Type: Article
    Journal or Publication Title: International Mathematics Research Notices
    Uncontrolled Keywords: Quantum stochastic cocycle, CCR flow, E-semigroup,operator space, operator system, matrix space, completely bounded, completely positive. ; CCR flow ; E-semigroup ; operator space ; operator system ; matrix space ; completely bounded ; completely positive
    Subjects:
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 58420
    Deposited By: ep_importer_pure
    Deposited On: 18 Sep 2012 12:09
    Refereed?: Yes
    Published?: Published
    Last Modified: 11 Jul 2014 16:47
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/58420

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