In this paper, we prove that the system formed by some of generalized eigenvectors of the operator T 0 + εT 1 + ε 2 T 2 + · · · which are analytic on ε, forms a Riesz basis of the separable Hilbert space H, where ε ∈ C and T 0 , T 1 , T 2 , . . . some linear transformations on H which have the same domain D ⊆ H. After that, we give an application for a problem concerning the radiation of a vibrating structure in a light fluid.
This paper is devoted to the investigation of the essential approximate point spectrum and the essential defect spectrum of a 2 × 2 block operator matrix on a product of Banach spaces. The obtained results are applied to a two-group transport operators with general boundary conditions in the Banach space Lp([−a, a] × [−1, 1]) × Lp([−a, a] × [−1, 1]), a > 0, p ≥ 1.
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