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Journal of Inequalities and Applications
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Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory

Journal of Inequalities and Applications volume 2008, Article number: 852676 (2007) Cite this article

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 and Affiliations

  1. Department of Mathematics, Faculty of Science of Sfax, Sfax, 3018, Tunisia

    Boulbeba Abdelmoumen, Aref Jeribi & Maher Mnif

  2. Département des Sciences Exactes, Université 8 Mai 1945, BP 401, Guelma, 24000, Algeria

    Abdelkader Dehici

Authors
  1. Boulbeba Abdelmoumen
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  2. Abdelkader Dehici
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  3. Aref Jeribi
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  4. Maher Mnif
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Corresponding author

Correspondence to Aref Jeribi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abdelmoumen, B., Dehici, A., Jeribi, A. et al. Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory. J Inequal Appl 2008, 852676 (2007). https://doi.org/10.1155/2008/852676

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

Keywords

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