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

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

Received 15 January 2007; Accepted 4 September 2007

Academic Editor: Jonathan M. Borwein

Copyright © 2007 Abdelkader Dehici and Khaled Saoudi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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)).