Let T be a bounded operator on an infinite-dimensional Banach space X and Ω a compact subset of the semi-Fredholm domain of T. We construct a finite rank perturbation F such that min[dim N(T+F-λ), codim R(T+F-λ)] = 0 for all λ ∈ Ω, and which is extremal in the sense that F² = 0 and rank F = max{min[dim N(T-λ), codim R(T-λ)] : λ ∈ Ω.
@article{bwmeta1.element.bwnjournal-article-smv129i3p253bwm,
author = {Thorsten Kr\"oncke},
title = {Extremal perturbations of semi-Fredholm operators},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {253-264},
zbl = {0941.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p253bwm}
}
Kröncke, Thorsten. Extremal perturbations of semi-Fredholm operators. Studia Mathematica, Tome 129 (1998) pp. 253-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv129i3p253bwm/
[00000] [Bo88] Z. Boulmaarouf, The Laffey-West decomposition, Proc. Roy. Irish Acad. Sect. A 88 (1988), 125-131. | Zbl 0675.47008
[00001] [Bo90] Z. Boulmaarouf, Décomposition de Laffey-West globale, thèse, l'Université de Nice, 1990.
[00002] [FöJa92] K.-H. Förster and K. Jahn, Extremal compressions and perturbations of bounded operators, ibid. 92 (1992), 289-296. | Zbl 0791.47006
[00003] [FöKr96] K.-H. Förster and M. Krause, On extremal perturbations of semi-Fredholm operators, Integral Equations Operator Theory 26 (1996), 125-135. | Zbl 0864.47003
[00004] [Is87] G. G. Islamov, Control of the spectrum of a dynamical system, Differential Equations 23 (1987), 872-875. | Zbl 0681.93038
[00005] [Ka58] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261-322. | Zbl 0090.09003
[00006] [Ka66] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
[00007] [Kr95] T. Kröncke, Extremale Störungen von Fredholmoperatoren, Diplomarbeit, Technische Universität Berlin, 1995.
[00008] [LaWe82] T. J. Laffey and T. T. West, Fredholm commutators, Proc. Roy. Irish Acad. Sect. A 87 (1987), 137-146.
[00009] [MaSe78] A. S. Markus and A. A. Sementsul, Operators which weakly perturb the spectrum, Sibirsk. Mat. Zh. 19 (1978), 646-653 (in Russian).
[00010] [Mb93] M. Mbekhta, Semi-Fredholm perturbations and commutators, Math. Proc. Cambridge Philos. Soc. 113 (1993), 173-177.
[00011] [Ó S88] M. Ó Searcóid, Economical finite rank perturbations of semi-Fredholm operators, Math. Z. 198 (1988), 431-434.
[00012] [Sł86] Z. Słodkowski, Operators with closed ranges in spaces of analytic vector-valued functions, J. Funct. Anal. 69 (1986), 155-177. | Zbl 0611.46046
[00013] [We90] T. T. West, Removing the jump-Kato's decomposition, Rocky Mountain J. Math. 20 (1990), 603-612. | Zbl 0726.47006
[00014] [Ze92] J. Zemánek, An analytic Laffey-West decomposition, Proc. Roy. Irish Acad. Sect. A 92 (1992), 101-106. | Zbl 0785.47008