No CrossRef data available.
Article contents
Perturbations by operators converging compactly to zero
Published online by Cambridge University Press: 24 October 2008
Abstract
This paper considers perturbations in locally convex spaces of semi Fredholm operators T by a sequence of operators {Kn} converging compactly to zero in a sense extending that from (2). It is shown that, under suitable conditions, α(T + Kn) ≤ α(T), β(T + Kn) ≤ β;(T) and κ(T + Kn) = κ(T) for large n.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 387 - 391
- Copyright
- Copyright © Cambridge Philosophical Society 1977
References
REFERENCES
(1)Browder, F.Functional analysis and partial differential equations I. Math. Ann. 138 (1959), 55–79.CrossRefGoogle Scholar
(2)Goldberg, S.Perturbations of semi Fredholm operators by operators converging to zero compactly. Proc. Amer. Math. Soc. 45 (1974), 93–98.Google Scholar
(3)Köthe, G.Topological vector spaces, vol. I, trans. Garling, D. J. H. (Springer, 1969).Google Scholar
(4)Pták, V.Completeness and the open mapping theorem. Bull. Soc. Math. France 86 (1958), 41–74.Google Scholar
(6)Vladimirski, Ju. N.On Φ+-operators in locally convex spaces (Russian). Uspehi. Mat. Nauk 23 (1968), 175–176.Google Scholar
(7)Vladimirski, Ju. N.On bounded perturbations of Φ--operators in locally convex spaces, Dokl. Akad. Nauk SSSR 196 (1971), 263–265, translated in Soviet Math. Dokl. 12 (1971), 80–83.Google Scholar