International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 26254, 10 pages
doi:10.1155/2007/26254

Some remarks on perturbation classes of semi-Fredholm and Fredholm operators

Abdelkader Dehici1 and Khaled Saoudi2

1Département des Sciences Exactes, Université 8 Mai 1945, Guelma 24000, Algeria
 2Centre Universitaire de Khenchela, Route de Batna, El houria, 40004 Khenchela, Algeria

Abstract

We show the existence of Banach spaces X, Y such that the set of strictly singular operators 𝒮(X,Y) (resp., the set of strictly cosingular operators 𝒞𝒮(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 operators Φ+(X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ−(X,Y)).