On a formula for the jumps in the semi-Fredholm domain.

Vladimir Rakocevic

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Displaying similar documents to “On a formula for the jumps in the semi-Fredholm domain.”

Lower s-numbers and their asymptotic behaviour

Vladimir Rakočević, Jaroslav Zemánek (1988)

Studia Mathematica

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Geometric characteristic of semi-Fredholm operators and their asymptotic behaviour

Jaroslav Zemánek (1984)

Studia Mathematica

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Extremal perturbations of semi-Fredholm operators

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.

Economical Finite Rank Perturbations of Semi-Fredholm Operators.

Micheál Ó. Searcóid (1988)

Mathematische Zeitschrift

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Operational quantities characterizing semi-Fredholm operators.

Manuel González, Antonio Martinón (1993)

Extracta Mathematicae

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Characterisations of open multivalued linear operators

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.

Kato decomposition of linear pencils

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.

Fredholm determinants and the Evans function for difference equations

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.

Operational quantities characterizing semi-Fredholm operators

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.

Semi-Fredholm Operators and Sequence Conditions.

K.-H. Förster, E.-O. Liebetrau (1983)

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Semi-Fredholm operators and perturbations.

Živković, Snežana (1997)

Publications de l'Institut Mathématique. Nouvelle Série

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Semi-Browder operators and perturbations

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].