On Lehner's `free' noncommutative analogue of the de Finetti theorem

Claus Köstler

On Lehner's `free' noncommutative analogue of the de Finetti theorem

Claus Köstler

Department of Physics

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Abstract

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.

Original language	English
Pages (from-to)	885-895
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	139
Publication status	Published - 31 Jan 2011

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On Lehner's `free' noncommutative analogue of De Finetti's theoremFinal published version, 155 KB

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abstract = "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.",

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AB - 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.

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On Lehner's `free' noncommutative analogue of the de Finetti theorem

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Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains

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On Lehner's `free' noncommutative analogue of the de Finetti theorem

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Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains

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