Abstract
The main goal of this paper is to give a characterization of the essential pseudospectra of \(2\times 2\) matrix of linear relations on a Banach space. We start by giving the definition and we investigate the characterization and some properties of the essential pseudospectra. Furthermore, we apply the obtained result to determine the essential pseudospectra of two-group transport equation with general boundary conditions in the Banach space.
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