## Abstract

We study the limit behaviour of T^{ k} f and of Cesaro averages A_{ n} f of this sequence, when T is order preserving and nonexpansive in L_{ 1}^{ +} . If T contracts also the L_{ ∞}-norm, the sequence T^{ n} f converges in distribution, and A_{ n} f converges weakly in L_{ p} (1<p<∞), and also in L_{ 1} if the measure is finite. "Speed limit" operators are introduced to show that strong convergence of A_{ n} f need not hold. The concept of convergence in distribution is extended to infinite measure spaces.

Original language | English |
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Pages (from-to) | 170-192 |

Number of pages | 23 |

Journal | Israel Journal of Mathematics |

Volume | 58 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jun 1987 |

## ASJC Scopus subject areas

- Mathematics (all)

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