Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Homomorphic Feller cocycles on a C*-algebra.
AU - Lindsay, J. Martin
AU - Wills, Stephen J.
N1 - RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
PY - 2003/8/1
Y1 - 2003/8/1
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.
U2 - 10.1112/S0024610703004174
DO - 10.1112/S0024610703004174
M3 - Journal article
VL - 68
SP - 255
EP - 272
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 1469-7750
IS - 1
ER -