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CHARACTERIZATIONS OF STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS BY PERTURBATION CLASSES

  • PIETRO AIENA (a1), MANUEL GONZÁLEZ (a2) and ANTONIO MARTÍNEZ-ABEJÓN (a3)
Abstract
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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References
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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