On completeness of spectral subspaces of linear relations and ordered pairs of linear operators

We study various conditions for a system of generalized eigenvectors and/or spectral subspaces of a linear operator, a linear pencil or a linear relation in a Banach space to be complete or form a basis. We use the spectral theory of linear relations, ergodic theorems, Phragmén–Lindelöf type results, and the method of similar operators.