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An isomorphism of quantum semimartingale algebras

Research output: Contribution to journalJournal article


Journal publication date06/2004
JournalThe Quarterly Journal of Mathematics
Number of pages31
Original languageEnglish


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.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics