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

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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.

Original languageEnglish (US)
Pages (from-to)2401-2409
Number of pages9
JournalProceedings of the American Mathematical Society
Volume140
Issue number7
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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