Extremal perturbations of semi-Fredholm operators

Thorsten Kröncke

Studia Mathematica (1998)

  • Volume: 129, Issue: 3, page 253-264
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Kröncke, Thorsten. "Extremal perturbations of semi-Fredholm operators." Studia Mathematica 129.3 (1998): 253-264. <http://eudml.org/doc/216503>.

@article{Kröncke1998,
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.},
author = {Kröncke, Thorsten},
journal = {Studia Mathematica},
keywords = {semi-Fredholm operators; minimum index; extremal perturbations; semi-Fredholm domain; finite rank operators},
language = {eng},
number = {3},
pages = {253-264},
title = {Extremal perturbations of semi-Fredholm operators},
url = {http://eudml.org/doc/216503},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Kröncke, Thorsten
TI - Extremal perturbations of semi-Fredholm operators
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 3
SP - 253
EP - 264
AB - 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.
LA - eng
KW - semi-Fredholm operators; minimum index; extremal perturbations; semi-Fredholm domain; finite rank operators
UR - http://eudml.org/doc/216503
ER -

References

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  12. [Ó S88] M. Ó Searcóid, Economical finite rank perturbations of semi-Fredholm operators, Math. Z. 198 (1988), 431-434. 
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  14. [We90] T. T. West, Removing the jump-Kato's decomposition, Rocky Mountain J. Math. 20 (1990), 603-612. Zbl0726.47006
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