On an estimate of the eigenvalues for an infinite-dimensional matrix and its application to the problem of the completeness of an eigenvector system of a completely continuous operator Original Research Article

We consider spectral properties of several infinite-dimensional matrices and show that matrices of this type can be used as a representative model for the Gram operator of a sesquilinear form. The representation is applied to the study of the completeness problem of an eigenvector system for a G-self-adjoint operator.