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Inspired by Lehner's results on exchangeability systems in [Leh06] we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two properties are equivalent and thus the process embeds into a von Neumann algebraic amalgamated free product over the fixed point algebra of the stationary process.
|Number of pages||11|
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 31 Jan 2011|
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Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains
Engineering and Physical Sciences Research Council
01 Jun 2009 → 31 May 2012
Project: Externally funded research