Displaying similar documents to “Fredholm, Riesz and local spectral theory of multipliers.”

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.

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.

Decomposable multipliers and applications to harmonic analysis

Kjeld Laursen, Michael Neumann (1992)

Studia Mathematica

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For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves...

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...