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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
Posted:
December 7, 2011
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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:
http://dx.doi.org/10.1090/S0002-9939-2011-11483-7
PII:
S 0002-9939(2011)11483-7
Keywords:
Semifinite von Neumann algebra,
uniform equicontinuity,
non-commu- tative ergodic theorem
Received by editor(s):
February 20, 2011
Posted:
December 7, 2011
Communicated by:
Marius Junge
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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