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Perturbation theory, M-essential spectra of 2 x 2 operator matrices and application to transport operators

Jeribi Aref, Moalla Nedra, Yengui Sonia

Journal of Mathematics and Applications

2021

Vol. 44

35--55

In this article we give some results on perturbation theory of 2 x 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 Lp([-a, a] x [-1, 1]) x Lp([-a, a] x [-1, 1]), p ≥ 1 and a > 0.