Perturbation classes for semi-Fredholm operators on subprojective and superprojective spaces

Abstract

We prove that the component P'+(X;Y ) of the perturbation class for the up- per semi-Fredholm operators between Banach spaces X and Y coincide with the strictly singular operators when every closed infinite dimensional subspace of X contains an infinite dimensional complemented subspace whose complement is isomorphic to X. Similarly, we prove that the com- ponent P'i(X;Y ) of the perturbation class for the lower semi-Fredholm operators coincide with the strictly cosingular operators when every infinite codimensional subspace of Y is contained in an infinite codimensional complemented subspace isomorphic to Y. We also give examples of Banach spaces satisfying the aforementioned conditions.