Displaying similar documents to “Banach spaces with small Calkin algebras”

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...

Calkin algebras for Banach spaces with finitely decomposable quotients

Manuel González, José M. Herrera (2003)

Studia Mathematica

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For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information...

On regularities and Fredholm theory

L. Lindeboom, H. Raubenheimer (2002)

Czechoslovak Mathematical Journal

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We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.

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...

Closed operators affiliated with a Banach algebra of operators

Bruce Barnes (1992)

Studia Mathematica

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Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.