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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

References

1. Birkhoff, G., Orthogonality in linear metric spaces, Duke Math. J. 1 (1935), 169-172.Google Scholar
2. Dunford, N. et Schwartz, J., Linear Operators I (Interscience, New York, 1964).Google Scholar
3. Foguel, S. R., A counterexample to a problem of Sz-Nagy, Proc. Amer. Math. Soc. 15 (1964), 788-790.Google Scholar
4. Goldberg, S., Unbounded Linear Operators (McGraw-Hill, New York, 1966).Google Scholar
5. Halmos, P. R., A Hilbert Space Problem Book (Van Nostrand, Princeton, 1967).Google Scholar
6. Halmos, P. R., On Foguel's answer to Nagy's question, Proc. Amer. Math. Soc. 15 (1964), 791-793.Google Scholar
7. Heuser, H., Funktionalanalysis (Teubner, Stuttgart, 1975).Google Scholar
8. Kurepa, S., Some properties of the spectral radius on a finite set of operators, Glasnik Mat. Ser. III 14(34), (1979), 283-288.Google Scholar
9. Mott, J. L., et Schneider, H., Matrix algebras and groups relatively bounded in norm, Arch. Math. 10 (1959), 1-6.Google Scholar
10. Rota, G. C., On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469-472.Google Scholar
11. Taylor, A. E., Introduction to Functional Analysis, (Wiley, New York, 1966).Google Scholar