Abstract
In this paper, we use the concept of demicompactness, introduced by Petryshyn [Construction of fixed points of demicompact mappings in Hilbert space. J Math Anal Appl. 1966;14:276–284], in order to give a new characterization of the essential spectra of a block operator matrix and to develop some perturbation results. Furthermore, we apply the obtained results to study some systems of differential equations and investigate the essential spectrum of two-groups of transport operators.
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