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CHARACTERIZATIONS OF STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS BY PERTURBATION CLASSES
Published online by Cambridge University Press: 02 August 2011
Abstract
We consider a class of operators that contains the strictly singular operators and it is contained in the perturbation class of the upper semi-Fredholm operators PΦ+. We show that this class is strictly contained in PΦ+, solving a question of Friedman. We obtain similar results for the strictly cosingular operators
and the perturbation class of the lower semi-Fredholm operators PΦ−. We also characterize
in terms of PΦ+ and
in terms of PΦ−. As a consequence, we show that
and
are the biggest operator ideals contained in PΦ+ and PΦ−, respectively.
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- Research Article
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- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2011
References
REFERENCES
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