### Abstract

In this paper we will examine the asymptotic behaviour of the iterates of linear maps
A : Rn ¿ Rn that are nonexpansive (contractive) with respect to a classical p-norm on Rn.
As a main result it will be shown that if 1 ?? p ?? 8 and p /= 2, there exists an integer q ?? 1
such that the sequence (Akqx)k is convergent for each x ¿ Rn. Moreover the integer q is the order, or twice the order, of a permutation on n letters.

Original language | English |
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Pages (from-to) | 265-276 |

Journal | Linear Algebra and Its Applications |

Volume | 371 |

DOIs | |

Publication status | Published - 2003 |

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## Cite this

Lemmens, B., & Gaans, van, O. W. (2003). Iteration of linear p-norm nonexpansive maps.

*Linear Algebra and Its Applications*,*371*, 265-276. https://doi.org/10.1016/S0024-3795(03)00454-3