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


Author: Claus Köstler
Journal: Proc. Amer. Math. Soc. 139 (2011), 885-895
MSC (2000): Primary 46L54; Secondary 46L53, 60G09
DOI: https://doi.org/10.1090/S0002-9939-2010-09926-2
Published electronically: October 22, 2010
MathSciNet review: 2745641
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Abstract | References | Similar Articles | Additional Information

Abstract: Inspired by Lehner's results on exchangeability systems, 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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Additional Information

Claus Köstler
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Address at time of publication: Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth, Wales SY23 3BZ
Email: koestler@uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-09926-2
Keywords: Noncommutative de Finetti theorem, distributional symmetries, noncommutative conditional independence, mean ergodic theorem, noncommutative Bernoulli shifts
Received by editor(s): June 25, 2008
Received by editor(s) in revised form: February 15, 2009
Published electronically: October 22, 2010
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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