Displaying similar documents to “A note on regular elements in Calkin algebras.”

Banach spaces with small Calkin algebras

Manuel González (2007)

Banach Center Publications

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Let X be a Banach space. Let 𝓐(X) be a closed ideal in the algebra ℒ(X) of the operators acting on X. We say that ℒ(X)/𝓐(X) is a Calkin algebra whenever the Fredholm operators on X coincide with the operators whose class in ℒ(X)/𝓐(X) is invertible. Among other examples, we have the cases in which 𝓐(X) is the ideal of compact, strictly singular, strictly cosingular and inessential operators, and some other ideals introduced as perturbation classes in Fredholm theory. Our aim is to...

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.

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...

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.

Fredholm multipliers of semisimple commutative Banach algebras.

Pietro Aiena (1991)

Extracta Mathematicae

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In some recent papers ([1],[2],[3],[4]) we have investigated some general spectral properties of a multiplier defined on a commutative semi-simple Banach algebra. In this paper we expose some aspects concerning the Fredholm theory of multipliers.