Riesz completeness of the eigenelements and associated elements of linear selfadjoint pencils

Methods of the theory of interpolation of Banach spaces are applied to the study of the following questions: Riesz completeness for linear pencils; selection of maximal semidefinite invariant subspaces for a given operator defined in a Krein space; boundedness of the Riesz projections corresponding to the unbounded component of the spectrum of a positive operator.