Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 852676, 14 pages
doi:10.1155/2008/852676
Research Article

Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory

Boulbeba Abdelmoumen,1 Abdelkader Dehici,2 Aref Jeribi,1 and Maher Mnif1

1Department of Mathematics, Faculty of Science of Sfax, Sfax 3018, Tunisia
2Département des Sciences Exactes, Université 8 Mai 1945, BP 401, Guelma 24000, Algeria

Received 19 April 2007; Revised 11 July 2007; Accepted 24 September 2007

Academic Editor: Nikolaos S. Papageorgiou

Copyright © 2008 Boulbeba Abdelmoumen et al. 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

The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish a fine description of the Schechter essential spectrum of a closed densely defined operators. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator.