Generalization of method A. A. Dorodnicyn close calculation of eigenvalues and eigenvectors of symmetric matrices on case of self-conjugate discrete operators

Let the discrete self-conjugate operator $A$ operates in separable Hilbert space $\mathbb H$ and has the kernel resolvent with simple spectrum. Self-conjugate and limited operator $B$ operates also in $\mathbb H$. Then it is possible to find such number $\varepsilon>0$, that eigenvalues and eigenfunctions of the perturbation operator $A+\varepsilon B$ will be calculated on a method of Dorodnicyn.