ON THE PERTURBATION CLASSES OF CONTINUOUS SEMI-FREDHOLM OPERATORS

We prove that the perturbation class of the upper semi-Fredholm operators from X into Y is the class of the strictly singular operators, whenever X is separable and Y contains a complemented copy of C[0, 1]. We also prove that the perturbation class of the lower semi-Fredholm operators from X into Y is the class of the strictly cosingular operators, whenever X contains a complemented copy of l_1 and Y is separable. We can remove the separability requirements by taking suitable spaces instead of C[0, 1] or l_1.