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Quasifree martingales

Lindsay, J. Martin...

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Quasifree martingales by Lindsay, J. Martin ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	27-07-2023
Summary	A noncommutative Kunita-Watanabe-type representation theorem is established for the martingales of quasifree states of CCR algebras. To this end the basic theory of quasifree stochastic integrals is developed using the abstract It\^o integral in symmetric Fock space, whose interaction with the operators of Tomita-Takesaki theory we describe. Our results extend earlier quasifree martingale representation theorems in two ways: the states are no longer assumed to be gauge-invariant, and the multiplicity space may now be infinite-dimensional. The former involves systematic exploitation of Araki's Duality Theorem. The latter requires the development of a transpose on matrices of unbounded operators, defying the lack of complete boundedness of the transpose operation.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1203.6693

Citation

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AMA 11th EditionReferences

Lindsay, J. Martin. Quasifree martingales. Australian National University. July 27, 2023. Accessed August 08, 2025. https://online.provdatabase.com/cite/5377

APA 7th EditionReferences

Lindsay, J. Martin. (2023). Quasifree martingales. Australian National University. https://online.provdatabase.com/cite/5377

Chicago 17th EditionReferences

Lindsay, J. Martin. Quasifree martingales. Australian National University. 2023. https://online.provdatabase.com/cite/5377

HarvardReferences

Lindsay, J. Martin. (2023). Quasifree martingales. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/5377. (Accessed 08 August 2025).

Harvard AustraliaReferences

Lindsay, J. Martin, 2023, Quasifree martingales, Australian National University, viewed 08 August 2025, <https://online.provdatabase.com/cite/5377>

MLA 9th EditionWorks Cited

Lindsay, J. Martin. Quasifree martingales. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/5377.

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