International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 26254, 10 pages
Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators
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.
We show the existence of Banach spaces , such that the set of strictly singular operators (resp., the set of strictly cosingular operators would be strictly included in
(resp., for the nonempty class of closed densely defined upper semi-Fredholm operators (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators .