Abdelmoumen, Boulbeba; Dehici, Abdelkader; Jeribi, Aref; Mnif, Maher Some new properties in Fredholm theory, Schechter essential spectrum, and application to transport theory. (English) Zbl 1151.47018 J. Inequal. Appl. 2008, Article ID 852676, 14 p. (2008). The authors give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, they establish a fine description of the Schechter essential spectrum of closed densely defined operators on an infinite-dimensional Banach space. These results are exploited to investigate the Schechter essential spectrum of a multidimensional neutron transport operator. Reviewer: Mohamed Zohry (Tétouan) Cited in 10 Documents MSC: 47A53 (Semi-) Fredholm operators; index theories 47A10 Spectrum, resolvent 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47N55 Applications of operator theory in statistical physics (MSC2000) 82D75 Nuclear reactor theory; neutron transport Keywords:measure of noncompactness; semi-Fredholm operator; Fredholm operator; Schechter essential spectrum PDFBibTeX XMLCite \textit{B. Abdelmoumen} et al., J. Inequal. Appl. 2008, Article ID 852676, 14 p. (2008; Zbl 1151.47018) Full Text: DOI EuDML References: [7] doi:10.2307/1989960 · Zbl 0023.32902 · doi:10.2307/1989960 [11] doi:10.1007/BF02052728 · Zbl 0203.45601 · doi:10.1007/BF02052728 [14] doi:10.1016/0022-247X(69)90217-0 · Zbl 0189.44104 · doi:10.1016/0022-247X(69)90217-0 [17] doi:10.1016/S0022-247X(02)00115-4 · Zbl 1042.47002 · doi:10.1016/S0022-247X(02)00115-4 [18] doi:10.1007/s10440-005-9005-2 · Zbl 1097.47014 · doi:10.1007/s10440-005-9005-2 [19] doi:10.2307/1996228 · Zbl 0255.47025 · doi:10.2307/1996228 [21] doi:10.1006/jmaa.1999.6314 · Zbl 0930.47008 · doi:10.1006/jmaa.1999.6314 [22] doi:10.1006/jmaa.2000.7121 · Zbl 0976.47008 · doi:10.1006/jmaa.2000.7121 [23] doi:10.1006/jmaa.1998.6038 · Zbl 0927.47007 · doi:10.1006/jmaa.1998.6038 [24] doi:10.1023/B:ACAP.0000026695.86402.1c · Zbl 1066.47039 · doi:10.1023/B:ACAP.0000026695.86402.1c This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.