  The spectral theory for operator pencils and operator differential-algebraic
equations is studied. Special focus is laid on singular operator pencils and
three different concepts of singular operator pencils are introduced. The
concepts are analyzed in detail and examples are presented that illustrate the
subtle differences. It is investigated how these concepts are related to
uniqueness of the underlying algebraic-differential operator equation, showing
that, in general, classical results known from the finite dimensional case of
matrix pencils and differential-algebraic equations do not prevail. The results
are then studied in the setting of structured operator pencils arising in
dissipative differential-algebraic equations. Here, unlike in the general
infinite-dimensional case, the uniqueness of solutions is closely related to
the singularity of the pencil.
