Peer-Reviewed Journal Details
Mandatory Fields
Lindsay, J. Martin; Wills, Stephen J. ;
2003
January
Journal of The London Mathematical Society
Homomorphic Feller cocycles on a C*-algebra.
Published
()
Optional Fields
Noncommutative probability, Markovian cocycles, Feller property, quantum stochastic, completely bounded, matrix spaces, dilation.
68 (2)
1
255
272
When a Fock-adapted Feller cocycle on a C*-algebra is regular, completely positive and contractive, it possesses a stochastic generator that is necessarily completely bounded. Necessary and sufficient conditions are given, in the form of a sequence of identities, for a completely bounded map to generate a weakly multiplicative cocycle. These are derived from a product formula for iterated quantum stochastic integrals. Under two alternative assumptions, one of which covers all previously considered cases, the first identity in the sequence is shown to imply the rest.
https://doi-org.ucc.idm.oclc.org/10.1112/S0024610703004174
Grant Details