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Uniform equicontinuity of sequences of measurable operators and non-commutative ergodic theorems


Author: Semyon Litvinov
Journal: Proc. Amer. Math. Soc. 140 (2012), 2401-2409
MSC (2010): Primary 46L51; Secondary 47A35
DOI: https://doi.org/10.1090/S0002-9939-2011-11483-7
Published electronically: December 7, 2011
MathSciNet review: 2898702
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Abstract: The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform equicontinuity in measure at zero on a dense subset implies the uniform equicontinuity in measure at zero on the entire space, which is then applied to derive some non-commutative ergodic theorems.


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Additional Information

Semyon Litvinov
Affiliation: Department of Mathematics, Pennsylvania State University, 76 University Drive, Hazleton, Pennsylvania 18202
Email: snl2@psu.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11483-7
Keywords: Semifinite von Neumann algebra, uniform equicontinuity, non-commu- tative ergodic theorem
Received by editor(s): February 20, 2011
Published electronically: December 7, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.