Belton, Alexander C. R. and Wills, Stephen J.
(2015)
*An algebraic construction of quantum flows with unbounded generators.*
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 51 (1).
pp. 349-375.
ISSN 0246-0203

## Abstract

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of a classical Feller process and semigroup from a given generator. The construction is possible provided the generator satisfies an invariance property for some dense subalgebra A_0 of the C* algebra A and obeys the necessary structure relations; the iterates of the generator, when applied to a generating set for A_0, must satisfy a growth condition. Furthermore, it is assumed that either the subalgebra A_0 is generated by isometries and A is universal, or A_0 contains its square roots. These conditions are verified in four cases: classical random walks on discrete groups, Rebolledo's symmetric quantum exclusion processes and flows on the non-commutative torus and the universal rotation algebra.

Item Type: | Journal Article |
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Journal or Publication Title: | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques |

Uncontrolled Keywords: | /dk/atira/pure/researchoutput/libraryofcongress/qa |

Subjects: | |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 65884 |

Deposited By: | ep_importer_pure |

Deposited On: | 06 Aug 2013 09:22 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 01 Jan 2020 08:05 |

URI: | https://eprints.lancs.ac.uk/id/eprint/65884 |

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