Skip to content


  • Research Article
  • Open Access

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

  • 1,
  • 2,
  • 1Email author and
  • 1
Journal of Inequalities and Applications20072008:852676

  • Received: 19 April 2007
  • Accepted: 24 September 2007
  • Published:


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.


  • Functional Analysis
  • Operator Theory
  • Full Article
  • Essential Spectrum
  • Fredholm Operator

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

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


© 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.