Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 852676, 14 pages
Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory
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.
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.