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Opérateurs à Itérés Uniformement Bornés
Published online by Cambridge University Press: 20 November 2018
Résumé
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Dans un espace de Banach complexe (X, | |) on considère un opérateur linéaire borné A de spectre σ(A) et de rayon spectral r(A) = 1. On établit des conditions, en termes du spectre périphérique de A: σπ(A) = {λ ∊ σ(A): |λ| = 1}, qui garantissent l'existence d'une norme | |0, équivalente à | |, définie par un produit scalaire si | | l'est et telle que ‖A‖0 = Sup{|Ax|0: x|0 = 1} = 1. Si A est à itérés uniformément bornés (‖An‖ ≤ M pour n = 1, 2, …) une telle norme peut ne pas exister.
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- Copyright © Canadian Mathematical Society 1982
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