Quasifree martingales

Lindsay, J. Martin and Margetts, Oliver T. (2013) Quasifree martingales. Journal of Functional Analysis. ISSN 0022-1236

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Abstract

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 Ito 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.

Item Type:	Article
Journal or Publication Title:	Journal of Functional Analysis
Uncontrolled Keywords:	Noncommutative probability, quantum stochastic, quantum martingale,
Subjects:	Q Science > QA Mathematics
Departments:	Faculty of Science and Technology > Mathematics and Statistics
ID Code:	58400
Deposited By:	ep_importer_pure
Deposited On:	12 Sep 2012 17:14
Refereed?:	Yes
Published?:	Published
Last Modified:	14 Sep 2012 17:03
Identification Number:
URI:	http://eprints.lancs.ac.uk/id/eprint/58400

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