Belton, Alexander C. R. (2004) An isomorphism of quantum semimartingale algebras. The Quarterly Journal of Mathematics, 55 (2). pp. 135-165.Full text not available from this repository.
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.
|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|
|Deposited On:||31 Mar 2008 14:42|
|Last Modified:||26 Jul 2012 16:19|
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