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Some new properties in Fredholm theory, Schechter essential spectrum, and application to transport theory. (English) Zbl 1151.47018

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.

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
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References:

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