Homomorphic Feller cocycles on a C*-algebra
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Date
2003-01
Authors
Lindsay, J. Martin
Wills, Stephen J.
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John Wiley & Sons, Inc.
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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.
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Keywords
Noncommutative probability , Markovian cocycles , Feller property , Quantum stochastic , Completely bounded , Matrix spaces , Dilation
Citation
Lindsay, J. M. and Wills, S. J. (2003) 'Homomorphic Feller Cocycles on a C*-Algebra', Journal of the London Mathematical Society, 68(2), pp. 255-272. doi: 10.1112/S0024610703004174
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© 2003, London Mathematical Society. Published by John Wiley & Sons Ltd. This is the accepted version of the following item: Lindsay, J. M. and Wills, S. J. (2003) 'Homomorphic Feller Cocycles on a C*-Algebra', Journal of the London Mathematical Society, 68(2), pp. 255-272, doi: 10.1112/S0024610703004174, which has been published in final form at: https://doi.org/10.1112/S0024610703004174. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.