## Abstract

Ornstein and Sucheston first proved that for a given positive contraction T: L _{1} → L _{1} there exists m 2 N such that if ∥T ^{m+1} - T ^{m} ∥ < 2, then lim _{n→∞} ∥T ^{n+1} -T ^{n} ∥ = 0. This result was referred to as the zero-two law. In the present article, we prove a generalized uniform zero-two law for the multipara- metric family of positive contractions of noncommutative L _{1} -spaces. Moreover, we also establish a vector-valued analogue of the uniform zero-two law for positive contractions of L _{1} (M; Φ)|the noncommutative L _{1} -spaces associated with center-valued traces.

Original language | English |
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Pages (from-to) | 600-616 |

Number of pages | 17 |

Journal | Banach Journal of Mathematical Analysis |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2018 |

## Keywords

- Bundle
- Noncommutative
- Positive contraction
- Zero-two law

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

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