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

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 un...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2012-07, Vol.140 (7), p.2401-2409
Main Author: LITVINOV, SEMYON
Format: Article
Language:English
Subjects:
Algebra
Ergodic theory
Linear transformations
Mathematical functions
Mathematical inequalities
Mathematical theorems
Perceptron convergence procedure
Topological theorems
Von Neumann algebra
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2011-11483-7