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EXISTENCE OF FELLER COCYCLES ON A C*-ALGEBRA

Published online by Cambridge University Press:  23 October 2001

J. MARTIN LINDSAY  and
STEPHEN J. WILLS
J. MARTIN LINDSAY
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD; [email protected], [email protected]
STEPHEN J. WILLS
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD; [email protected], [email protected]
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Abstract

The quantum stochastic differential equation dkt = kt ∘ θαβdΛβα(t) is considered on a unital C*-algebra, with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for the existence of a completely positive contractive solution are shown to be sufficient. It is known that for completely positive contraction processes, k satisfies such an equation if and only if k is a regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology if the algebra is thought of as a non-commutative topological space.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 5 , September 2001 , pp. 613 - 621
Copyright
© The London Mathematical Society 2001

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