Symmetric family of Fredholm operators of indices zero, stability of essential spectra and application to transport operators |
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Authors: | Faiçal Abdmouleh Aref Jeribi |
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Institution: | Département de Mathématiques, Université de Sfax, Faculté des Sciences de Sfax, Route de Soukra, Km 3,5, B.P. 1171, 3000, Sfax, Tunisia |
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Abstract: | In this paper, we prove that, if the product A=A1?An is a Fredholm operator where the ascent and descent of A are finite, then Aj is a Fredholm operator of index zero for all j, 1?j?n, where A1,…,An be a symmetric family of bounded operators. Next, we investigate a useful stability result for the Rako?evi?/Schmoeger essential spectra. Moreover, we show that some components of the Fredholm domains of bounded linear operators on a Banach space remain invariant under additive perturbations belonging to broad classes of operators A such as γ(Am)<1 where γ(⋅) is a measure of noncompactness. We also discuss the impact of these results on the behavior of the Rako?evi?/Schmoeger essential spectra. Further, we apply these latter results to investigate the Rako?evi?/Schmoeger essential spectra for singular neutron transport equations in bounded geometries. |
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Keywords: | Essential spectra Fredholm operators Semi-Fredholm operators Polynomially compact operators Measures of noncompactness in Banach spaces Transport equation |
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