26254 Research Article Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators (original) (raw)

We show the existence of Banach spaces X, Y such that the set of strictly singular oper-ators (X,Y) (resp., the set of strictly cosingular operators (X,Y)) would be strictly included in F+(X,Y) (resp., F−(X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operatorsΦ+(X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ−(X,Y)). Copyright © 2007 A. Dehici and K. Saoudi. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distri-bution, and reproduction in any medium, provided the original work is properly cited. 1.