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HOMOMORPHIC FELLER COCYCLES ON A $C^*$-ALGEBRA

Published online by Cambridge University Press:  08 August 2003

J. MARTIN LINDSAY  and
STEPHEN J. WILLS
J. MARTIN LINDSAY
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD [email protected]
STEPHEN J. WILLS
Affiliation:
Department of Mathematics, University College Cork, National University of Ireland, [email protected]
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Abstract

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.

Keywords

81S2560H2046L0746L5347D06
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 255 - 272
Copyright
The London Mathematical Society 2003

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