Displaying similar documents to “Extremal perturbations of semi-Fredholm operators”

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

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.

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.

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.

An Atkinson-type theorem for B-Fredholm operators

M. Berkani, M. Sarih (2001)

Studia Mathematica

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Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only...

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 derived from the norm and generalized Fredholm theory

Manuel Gonzalez, Antonio Martinón (1991)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study some operational quantities associated to a space ideal 𝔸 . These quantities are used to define generalized semi-Fredholm operators associated to 𝔸 , and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space...