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Opérateurs à Itérés Uniformement Bornés

Published online by Cambridge University Press:  20 November 2018

José I. Nieto
José I. Nieto*
Affiliation:
Université de Montréal Département de Mathématiques, et de Statistique Montréal, Québec H3C 3J7
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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.

Keywords

47A1047A3047B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 355 - 360
Copyright
Copyright © Canadian Mathematical Society 1982

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