Existence of Feller Cocycles on a C*-Algebra |
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Authors: | Lindsay, J. Martin Wills, Stephen J. |
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Affiliation: | School of Mathematical Sciences, University of Nottingham Nottingham NG7 2RD; jml{at}maths.nott.ac.uk, sjw{at}maths.nott.ac.uk |
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Abstract: | The quantum stochastic differential equation is considered on a unital C*-algebra, with separablenoise dimension space. Necessary conditions on the matrix ofbounded linear maps for the existence of a completely positivecontractive solution are shown to be sufficient. It is knownthat for completely positive contraction processes, k satisfiessuch an equation if and only if k is a regular Markovian cocycle.Feller refers to an invariance condition analogousto probabilistic terminology if the algebra is thought of asa non-commutative topological space. 2000 Mathematics SubjectClassification 81S25, 46L07, 46L53, 47D06. |
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