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

Full text not available from this repository.

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:
Journal Article
Journal or Publication Title:
The Quarterly Journal of Mathematics
Additional Information:
RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2600
Subjects:
?? general mathematicsmathematics(all)qa mathematics ??
ID Code:
2399
Deposited By:
Deposited On:
31 Mar 2008 13:42
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 08:26