Fredholm theory in Banach algebras
M. Smyth (1982)
Banach Center Publications
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M. Smyth (1982)
Banach Center Publications
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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...
Đorđević, Dragan (1994)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
Robin Harte (1982)
Mathematische Zeitschrift
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J. J. Grobler, H. Raubenheimer (2008)
Studia Mathematica
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We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.
Pietro Aiena (1994)
Extracta Mathematicae
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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...
Z. Słodkowski, W. Żelazko (1982)
Banach Center Publications
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Dehici, Abdelkader, Saoudi, Khaled (2007)
International Journal of Mathematics and Mathematical Sciences
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