On a Riesz basis of eigenvectors of a nonself-adjoint analytic operator and applications

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In the present paper, we deal with the perturbed operatorwhere is a closed densely defined linear operator on a separable Hilbert space X with domain while are linear operators on X with the same domain and satisfying a specific growing inequality. The basic idea here is to investigate under sufficient conditions assuring the existence of a Riesz basis of eigenvectors of the operator . The obtained results are of importance for application to a nonself-adjoint problem describing the radiation of a vibrating structure in a light fluid and to a nonself-adjoint Gribov operator in Bargmann space.