In this paper, we will establish some results on perturbation theory of block
operator matrices acting on Xn, where X is a Banach space. These results are
exploited to investigate the M-essential spectra of a general class of
operators defined by a 3x3 block operator matrix acting on a product of
Banach spaces X3.
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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