In this paper, we investigate the essential approximate point spectrum and the essential defect spectrum of a 2×2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to two-group transport operators in the Banach space
This paper gives a survey on some recent results on the spectral theory of block operator matrices. We study the closeness in the product space and we give some conditions to characterize the essential spectra in the Browder resolvent set case. Furthermore, we apply the obtained results to several models such as delay equations, Sturm-Liouville problem and transport equations.
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