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

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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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

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