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Tail algebras of quantum exchangeable random variables


Authors: Kenneth J. Dykema and Claus Köstler
Journal: Proc. Amer. Math. Soc. 142 (2014), 3853-3863
MSC (2010): Primary 46L53; Secondary 46L54, 81S25, 46L10
DOI: https://doi.org/10.1090/S0002-9939-2014-12116-2
Published electronically: June 27, 2014
MathSciNet review: 3251725
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Abstract: We show that any countably generated von Neumann algebra with specified normal faithful state can arise as the tail algebra of a quantum exchangeable sequence of noncommutative random variables. We also characterize the cases when the state corresponds to a limit of convex combinations of free product states.


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Additional Information

Kenneth J. Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: kdykema@math.tamu.edu

Claus Köstler
Affiliation: Institute of Mathematical and Physical Sciences, Aberystwyth University, Aberystwyth SY23 3BZ, Wales, United Kingdom
Email: cck@aber.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-12116-2
Keywords: Quantum exchangeable, de Finetti, amalgamated free product
Received by editor(s): February 21, 2012
Received by editor(s) in revised form: November 18, 2012
Published electronically: June 27, 2014
Additional Notes: The first author’s research was supported in part by NSF grant DMS-0901220
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society