On Lehner’s ‘free’ noncommutative analogue of de Finetti’s theorem
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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.References
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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
- MR Author ID: 639717
- Email: koestler@uiuc.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2745641