On a characterization of the S-essential spectra of the sum and the product of two operators and application to a transport operator

In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1 ([–a, a] × [–1, 1]) (a > 0).