TY - JOUR
T1 - Homomorphic Feller cocycles on a C*-algebra
AU - Lindsay, J. Martin
AU - Wills, Stephen J.
PY - 2003/8
Y1 - 2003/8
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/0042862848
U2 - 10.1112/S0024610703004174
DO - 10.1112/S0024610703004174
M3 - Article
AN - SCOPUS:0042862848
SN - 0024-6107
VL - 68
SP - 255
EP - 272
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 1
ER -