### 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 language | English (US) |
---|---|

Pages (from-to) | 2401-2409 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 7 |

DOIs | |

State | Published - Mar 29 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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**Uniform equicontinuity of sequences of measurable operators and non-commutative ergodic theorems.** / Litvinov, Semyon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uniform equicontinuity of sequences of measurable operators and non-commutative ergodic theorems

AU - Litvinov, Semyon

PY - 2012/3/29

Y1 - 2012/3/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84858810225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858810225&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2011-11483-7

DO - 10.1090/S0002-9939-2011-11483-7

M3 - Article

AN - SCOPUS:84858810225

VL - 140

SP - 2401

EP - 2409

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -