## Abstract

Akcoglu and Suchaston proved the following result: Let T : L ^{1}(X,F,μ) → L^{1}(X, F, μ) be a positive contraction. Assume that for z ∈ L^{1}(X,F,μ) the sequence (T^{n}z) converges weakly in L^{1}(X,F,μ). Then either lim_{n→∞} ∥T^{n}z∥ = 0 or there exists a positive function h ∈ L^{1}(X, F,μ),h ≠ 0 such that Th = h. In the paper we prove an extension of this result in a finite von Neumann algebra setting, and as a consequence we obtain that if a positive contraction of a noncommutative L^{1}-space has no nonzero positive invariant element, then its mixing property implies the completely mixing property.

Original language | English |
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Pages (from-to) | 843-850 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 134 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2006 |

Externally published | Yes |

## Keywords

- Completely mixing
- Mixing
- Non Neumann algebra
- Positive contraction

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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