On the basis property for a certain part of the eigenvectors and associated vectors of a selfadjoint operator pencil

Let $L(\lambda)=A+\lambda I+\lambda^2B$ be a quadratic pencil, where $A$ and $B$ are compact selfadjoint operators on a separable Hilbert space $\mathfrak H$. Two subsystems of eigenvectors and associated vectors are constructed for the pencil $L(\lambda)$, each of them forming a Riesz basis for $\mathfrak H$.
Bibliography: 24 titles.