Lower s-numbers and their asymptotic behaviour
Vladimir Rakočević, Jaroslav Zemánek (1988)
Studia Mathematica
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Vladimir Rakočević, Jaroslav Zemánek (1988)
Studia Mathematica
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Jaroslav Zemánek (1984)
Studia Mathematica
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Thorsten Kröncke (1998)
Studia Mathematica
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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.
Micheál Ó. Searcóid (1988)
Mathematische Zeitschrift
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Manuel González, Antonio Martinón (1993)
Extracta Mathematicae
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T. Álvarez (2006)
Studia Mathematica
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The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.
Dominique Gagnage (2003)
Studia Mathematica
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T. Kato [5] found an important property of semi-Fredholm pencils, now called the Kato decomposition. M. A. Kaashoek [3] introduced operators having the property P(S:k) as a generalization of semi-Fredholm operators. In this work, we study this class of operators. We show that it is characterized by a Kato-type decomposition. Other properties are also proved.
David Cramer, Yuri Latushkin (2007)
Banach Center Publications
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We develop a difference equations analogue of recent results by F. Gesztesy, K. A. Makarov, and the second author relating the Evans function and Fredholm determinants of operators with semi-separable kernels.
Manuel González, Antonio Martinón (1995)
Studia Mathematica
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Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
K.-H. Förster, E.-O. Liebetrau (1983)
Manuscripta mathematica
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Živković, Snežana (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Vladimir Rakočević (1997)
Studia Mathematica
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An operator in a Banach space is called upper (resp. lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (resp. descent). An operator in a Banach space is called semi-Browder if it is upper semi-Browder or lower semi-Browder. We prove the stability of the semi-Browder operators under commuting Riesz operator perturbations. As a corollary we get some results of Grabiner [6], Kaashoek and Lay [8], Lay [11], Rakočević [15] and Schechter [16].