Open Access

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

  • Boulbeba Abdelmoumen1,
  • Abdelkader Dehici2,
  • Aref Jeribi1Email author and
  • Maher Mnif1
Journal of Inequalities and Applications20072008:852676

https://doi.org/10.1155/2008/852676

Received: 19 April 2007

Accepted: 24 September 2007

Published: 2 December 2007

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science of Sfax
(2)
Département des Sciences Exactes

Copyright

© Boulbeba Abdelmoumen et al. 2008

This article is published under license to BioMed Central Ltd. 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.