Sesquilinear quantum stochastic analysis in Banach space

Lindsay, Martin and Das, Bata Krishna and Tripak, Orawan (2014) Sesquilinear quantum stochastic analysis in Banach space. Journal of Mathematical Analysis and Applications, 409 (2). pp. 1031-1051. ISSN 0022-247X

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Abstract

A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic Lie–Trotter product formula. The theory is used to extend, unify and refine standard quantum stochastic analysis through different choices of Banach space, of which there are three paradigm classes: spaces of bounded Hilbert space operators, operator mapping spaces and duals of operator space coalgebras. Our results provide the basis for a general theory of quantum stochastic processes in operator spaces, of which Lévy processes on compact quantum groups is a special case.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Additional Information:
The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 409 (2), 2013, © ELSEVIER.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
67165
Deposited By:
Deposited On:
14 Oct 2013 08:39
Refereed?:
Yes
Published?:
Published
Last Modified:
25 Oct 2020 02:34