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Quantum random walk approximation in Banach algebra

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<mark>Journal publication date</mark>1/10/2015
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number1
Number of pages18
Pages (from-to)465-482
Publication StatusPublished
Early online date19/02/15
<mark>Original language</mark>English


Abstract Belton's discrete approximation scheme is extended to Banach-algebra-valued sesquilinear quantum stochastic cocycles, through the dyadic discretisation of time. Approximation results for Markov-regular quantum stochastic mapping cocycles are recovered. We also obtain a new random walk approximation for a class of (not necessarily Markov-regular) isometric operator cocycles. Every Lévy process on a compact quantum group is implemented by a unitary cocycle from this class.