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An isomorphism of quantum semimartingale algebras

Belton, Alexander C. R. (2004) An isomorphism of quantum semimartingale algebras. The Quarterly Journal of Mathematics, 55 (2). pp. 135-165. ISSN 0033-5606

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Abstract

We give details of a *-linear bijection between adapted (in the sense of Hudson and Parthasarathy) and vacuum-adapted quantum stochastic integrals. This provides new insight into Attal's remarkable transformation of quantum semimartingales, by showing that it factorizes in a natural manner. The Banach *-algebras of regular quantum and Ω-semimartingales are consequently isomorphic, and an intrinsic characterisation of Ω-semimartingales is obtained as an application of this fact. Various formulae occurring in quantum stochastic calculus are shown to have a more natural appearance in the vacuum-adapted framework. We finish by providing the full generalization of this theory to higher dimensions.

Item Type: Article
Journal or Publication Title: The Quarterly Journal of Mathematics
Additional Information: RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 2399
Deposited By: ep_importer
Deposited On: 31 Mar 2008 14:42
Refereed?: Yes
Published?: Published
Last Modified: 19 Nov 2013 09:51
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/2399

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