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ArticleOriginal scientific text

Title

Extremal perturbations of semi-Fredholm operators

Authors 1

Affiliations

  1. Technische Universität Berlin, Fachbereich Mathematik, MA 7-5, Strasse des 17. Juni 136, D-10623 Berlin, Germany

Abstract

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.

Bibliography

  1. [Bo88] Z. Boulmaarouf, The Laffey-West decomposition, Proc. Roy. Irish Acad. Sect. A 88 (1988), 125-131.
  2. [Bo90] Z. Boulmaarouf, Décomposition de Laffey-West globale, thèse, l'Université de Nice, 1990.
  3. [FöJa92] K.-H. Förster and K. Jahn, Extremal compressions and perturbations of bounded operators, ibid. 92 (1992), 289-296.
  4. [FöKr96] K.-H. Förster and M. Krause, On extremal perturbations of semi-Fredholm operators, Integral Equations Operator Theory 26 (1996), 125-135.
  5. [Is87] G. G. Islamov, Control of the spectrum of a dynamical system, Differential Equations 23 (1987), 872-875.
  6. [Ka58] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261-322.
  7. [Ka66] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
  8. [Kr95] T. Kröncke, Extremale Störungen von Fredholmoperatoren, Diplomarbeit, Technische Universität Berlin, 1995.
  9. [LaWe82] T. J. Laffey and T. T. West, Fredholm commutators, Proc. Roy. Irish Acad. Sect. A 87 (1987), 137-146.
  10. [MaSe78] A. S. Markus and A. A. Sementsul, Operators which weakly perturb the spectrum, Sibirsk. Mat. Zh. 19 (1978), 646-653 (in Russian).
  11. [Mb93] M. Mbekhta, Semi-Fredholm perturbations and commutators, Math. Proc. Cambridge Philos. Soc. 113 (1993), 173-177.
  12. [Ó S88] M. Ó Searcóid, Economical finite rank perturbations of semi-Fredholm operators, Math. Z. 198 (1988), 431-434.
  13. [Sł86] Z. Słodkowski, Operators with closed ranges in spaces of analytic vector-valued functions, J. Funct. Anal. 69 (1986), 155-177.
  14. [We90] T. T. West, Removing the jump-Kato's decomposition, Rocky Mountain J. Math. 20 (1990), 603-612.
  15. [Ze92] J. Zemánek, An analytic Laffey-West decomposition, Proc. Roy. Irish Acad. Sect. A 92 (1992), 101-106.
Studia Mathematica
1998/129/3
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Pages:
253-264
Main language of publication
English
Received
1997-04-17
Accepted
1997-10-27
Published
1998
Exact and natural sciences