Abstract
Let {{mathcal {S}}}{{mathcal {S}}} and {{mathcal {S}}}{{mathcal {C}}} be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let PPhi _+ and PPhi _+ be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators Phi {mathcal {S}} and Phi {mathcal {C}} that satisfy {{mathcal {S}}}{{mathcal {S}}}subset Phi {mathcal {S}}subset PPhi _+ and {{mathcal {S}}}{{mathcal {C}}}subset Phi {mathcal {C}}subset PPhi _-. We give some conditions under which these inclusions become equalities, from which we derive some positive solutions to the perturbation classes problem for semi-Fredholm operators.
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