Displaying similar documents to “Best Fredholm perturbation theorems”

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...

Operational quantities derived from the norm and generalized Fredholm theory.

Manuel González, Antonio Martinón (1991)

Extracta Mathematicae

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Several operational quantities, defined in terms of the norm and the class of finite dimensional Banach spaces, have been used to characterize the classes of upper and lower semi-Fredholm operators, strictly singular and strictly cosingular operators, and to derive some perturbation results. In this paper we shall introduce and study some operational quantities derived from the norm and associated to a space ideal. By means of these quantities we construct a generalized...

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...