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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A noncommutative version of the John-Nirenberg theorem


Authors: Marius Junge and Magdalena Musat
Journal: Trans. Amer. Math. Soc. 359 (2007), 115-142
MSC (2000): Primary 46L52; Secondary 60G46
Published electronically: August 24, 2006
MathSciNet review: 2247885
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Abstract: We prove a noncommutative version of the John-Nirenberg theorem for nontracial filtrations of von Neumann algebras. As an application, we obtain an analogue of the classical large deviation inequality for elements of the associated $ BMO$ space.


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Additional Information

Marius Junge
Affiliation: Department of Mathematics, 1409 West Green Street, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: junge@math.uiuc.edu

Magdalena Musat
Affiliation: Department of Mathematics, 0112, 9500 Gilman Drive, University of California, San Diego, La Jolla, California 92093-0112
Address at time of publication: Department of Mathematical Sciences, The University of Memphis, 373 Dunn Hall, Memphis, Tennessee 38152
Email: mmusat@math.ucsd.edu, mmusat@memphis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03999-7
PII: S 0002-9947(06)03999-7
Keywords: Noncommutative $L_p$-spaces and $BMO$, noncommutative martingales, interpolation
Received by editor(s): October 4, 2004
Published electronically: August 24, 2006
Additional Notes: The first author was partially supported by the National Science Foundation, DMS-0301116.
Article copyright: © Copyright 2006 American Mathematical Society