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In this paper, we study the class of unbounded generalized meromorphic operators GM(E, ∞), where E is a finite subset of C, which generalizes the notion of unbounded meromorphic operators. More precisely, we give a decomposition and some characterizing properties of these operators based on the punctured neighborhood theorem and the operational calculus for unbounded operators.

In this paper, we give some results on the essential B-spectra of a linear operator pencil, which are used to determine the essential B-spectra of an integro-differential operator with abstract boundary conditions in the Banach space Lp([−a, a] × [−1, 1]), p ≥ 1 and a > 0.

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