Displaying similar documents to “Economical Finite Rank Perturbations of Semi-Fredholm Operators.”

Extremal perturbations of semi-Fredholm operators

Thorsten Kröncke (1998)

Studia Mathematica

Similarity:

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.

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

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

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

Similarity:

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.

An Atkinson-type theorem for B-Fredholm operators

M. Berkani, M. Sarih (2001)

Studia Mathematica

Similarity:

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...

Kato decomposition of linear pencils

Dominique Gagnage (2003)

Studia Mathematica

Similarity:

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

Similarity:

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.