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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 L  p ([−a, a] × [−1, 1]) × L  p ([−a, a] × [−1, 1]), a > 0, p ≥ 1.

On a characterization of the essential spectra of some matrix operators and application to two-group transport operators