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Iteration of linear p-norm nonexpansive maps

✍ Scribed by Bas Lemmens; Onno Van Gaans

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
128 KB
Volume
371
Category
Article
ISSN
0024-3795

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✦ Synopsis

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

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