Perturbation Theory, M-essential Spectra of 2⨯2 Operator Matrices and Application to Transport Operators

In this article we give some results on perturbation theory of 2⨯2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space L_p([-a, a] ⨯ [-1, 1]) ⨯ L_p([-a, a] ⨯ [-1, 1]), p ≥ 1 and a > 0.

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