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An isomorphism of quantum semimartingale algebras

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An isomorphism of quantum semimartingale algebras. / Belton, Alexander C. R.
In: The Quarterly Journal of Mathematics, Vol. 55, No. 2, 06.2004, p. 135-165.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Belton, ACR 2004, 'An isomorphism of quantum semimartingale algebras', The Quarterly Journal of Mathematics, vol. 55, no. 2, pp. 135-165. https://doi.org/10.1093/qmath/hag052

APA

Belton, A. C. R. (2004). An isomorphism of quantum semimartingale algebras. The Quarterly Journal of Mathematics, 55(2), 135-165. https://doi.org/10.1093/qmath/hag052

Vancouver

Belton ACR. An isomorphism of quantum semimartingale algebras. The Quarterly Journal of Mathematics. 2004 Jun;55(2):135-165. doi: 10.1093/qmath/hag052

Author

Belton, Alexander C. R. / An isomorphism of quantum semimartingale algebras. In: The Quarterly Journal of Mathematics. 2004 ; Vol. 55, No. 2. pp. 135-165.

Bibtex

@article{e35a23d58b26497b9d32e3d028567f00,
title = "An isomorphism of quantum semimartingale algebras",
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.",
author = "Belton, {Alexander C. R.}",
note = "RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics",
year = "2004",
month = jun,
doi = "10.1093/qmath/hag052",
language = "English",
volume = "55",
pages = "135--165",
journal = "The Quarterly Journal of Mathematics",
issn = "0033-5606",
publisher = "Oxford University Press",
number = "2",

}

RIS

TY - JOUR

T1 - An isomorphism of quantum semimartingale algebras

AU - Belton, Alexander C. R.

N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics

PY - 2004/6

Y1 - 2004/6

N2 - 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.

AB - 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.

U2 - 10.1093/qmath/hag052

DO - 10.1093/qmath/hag052

M3 - Journal article

VL - 55

SP - 135

EP - 165

JO - The Quarterly Journal of Mathematics

JF - The Quarterly Journal of Mathematics

SN - 0033-5606

IS - 2

ER -