publication . Article . 2000

Quantum Stochastic Calculus on Full Fock Modules

Skeide, Michael;
Open Access English
  • Published: 01 Jun 2000 Journal: Journal of Functional Analysis, issue 2, pages 401-452 (issn: 00221236, Copyright policy)
  • Publisher: Academic Press.
Abstract
Abstract We develop a quantum stochastic calculus on full Fock modules over arbitrary Hilbert B – B -modules. We find a calculus of bounded operators where all quantum stochastic integrals are limits of Riemann–Stieltjes sums. After having estalished existence and uniqueness of solutions of a large class of quantum stochastic differential equations, we find necessary and sufficient conditions for unitarity of a subclass of solutions. As an application we find dilations of a conservative CP-semigroup (quantum dynamical semigroup) on B with arbitrary bounded (Christensen–Evans) generator. We point out that in the case B = B ( G ) the calculus may be interpreted as...
Subjects
free text keywords: Analysis, Time-scale calculus, Quantum stochastic calculus, Quantum differential calculus, Matrix calculus, Mathematics, Fock space, Multivariable calculus, Topology, Algebra, Borel functional calculus, Mathematical analysis, Stochastic calculus
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publication . Article . 2000

Quantum Stochastic Calculus on Full Fock Modules

Skeide, Michael;