Peer-Reviewed Journal Details
Mandatory Fields
Lindsay, J. Martin; Wills, Stephen J. ;
2001
January
Bulletin Of The London Mathematical Society
Existence of Feller cocycles on a C*-algebra
Published
()
Optional Fields
Feller cocycle; Markovian cocycle; quantum stochastic differential equation; completely bounded; operator space
33
5
613
621
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.
0024-6093
https://doi.org/10.1112/S0024609301008128
Grant Details