Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

Dehici, Abdelkader; Saoudi, Khaled

doi:https://doi.org/10.1155/2007/26254

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 026254 | https://doi.org/10.1155/2007/26254

Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

Abdelkader Dehici¹and Khaled Saoudi²

Academic Editor: Jonathan M. Borwein

Received15 Jan 2007

Accepted04 Sept 2007

Published30 Oct 2007

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)).

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Copyright

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.

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