The perturbation classes problem for subprojective and superprojective Banach spaces

摘要

We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when Xis subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y. (C) 2020 Elsevier Inc. All rights reserved.