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A Short Proof of Vladimirskii′s Theorem on Precompact Perturbations in Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

Le Quang Chu
Le Quang Chu*
Affiliation:
Department of Mathematics, University of Saskatchewan Saskatoon, SaskatchewanCanada
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Let T, P denote two continuous operators from E into F, where E and F are locally convex spaces. It is proved by L. Schwartz [8] and G. KÖthe [6] that if E and F are Fréchet spaces, T is a ϕ_-operator and P a compact operator, then T+P is a ϕ_-operator.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 649 - 655
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. De Wilde, M., Perturbation of maps in locally convex spaces. Proceedings of the Analysis Conference, Rio 1972. Paris: Hermann, (to appear.)Google Scholar
2. De Wilde, M. and Chu, Le Quang, Perturbation of maps in locally convex spaces, Math,. Ann. 215, 215-233 (1975).Google Scholar
3. Gokhberg, I. C. and Krein, M. G., The basic propositions on defect numbers, root numbers and indices of linear operators, Amer. Math. Soc. Transi. (2), 13, 185-264 (1960).Google Scholar
4. Goldberg, S., Unbounded linear operators (theory and applications), McGraw-Hill, New York 1966.Google Scholar
5. Kato, T., Perturbation theory for mullity, deficiency and other quantities of linear operators, J. d'analyse Math. 6, 261-322 (1958).Google Scholar
6. Köthe, G., Zur ThÉorie der kompakten Operatoren in lokalkonvexen Räumen, Port. Math. 13, 3, 97-104 (1954).Google Scholar
7. Pietsch, A., Homomorphismen in lokalkonvexen Vektorräumen, Math. Nachr. 22, 3-4, 162-174 (1960).Google Scholar
8. Schwartz, L., Homomorphismes et applications complètement continues, C.R. Acad. Sc. Paris 236, 2472-2473 (1953).Google Scholar
9. Vladimirskii, Ju. N., On compact perturbations of Φ_-operators in locally convex spaces, (in Russian). Sib. Mat. Journal 14, 4, 738-759 (1973).Google Scholar