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A noncommutative version of the John-Nirenberg theorem

Author(s): Marius Junge; Magdalena Musat
Journal: Trans. Amer. Math. Soc. 359 (2007), 115-142.
MSC (2000): Primary 46L52; Secondary 60G46
Posted: August 24, 2006
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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: 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
Posted: August 24, 2006
Additional Notes: The first author was partially supported by the National Science Foundation, DMS-0301116.
Copyright of article: Copyright 2006, American Mathematical Society

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