Operational quantities characterizing semi-Fredholm operators.
Manuel González, Antonio Martinón (1993)
Extracta Mathematicae
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Manuel González, Antonio Martinón (1993)
Extracta Mathematicae
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Jaroslav Zemánek (1984)
Studia Mathematica
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Manuel González, Antonio Martinón (1995)
Studia Mathematica
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Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
Snežana Živković (2002)
Matematički Vesnik
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Manuel González, Antonio Martinón (1990)
Extracta Mathematicae
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L. A. Coburn, A. Lebow (1966)
Rendiconti del Seminario Matematico della Università di Padova
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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 . These quantities are used to define generalized semi-Fredholm operators associated to , 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...
Vladimir Rakočević (1997)
Studia Mathematica
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An operator in a Banach space is called upper (resp. lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (resp. descent). An operator in a Banach space is called semi-Browder if it is upper semi-Browder or lower semi-Browder. We prove the stability of the semi-Browder operators under commuting Riesz operator perturbations. As a corollary we get some results of Grabiner [6], Kaashoek and Lay [8], Lay [11], Rakočević [15] and Schechter [16].