This paper is concerned with stability analysis of
left and right Atkinson types of
unbounded linear operators on Banach spaces by using the measure
of non strict singularity. Under quite general assumptions, we first
present a new characterization on the left (right) Weyl spectra of
unbounded linear operators which will be used to prove certain
stability properties of left (right) Weyl operators with
perturbation. Therefore, a new description of left (right) Weyl
spectra of unbounded operator matrices with non maximal domain is
presented to reach the validity of the theoretical results which led
to significant advances in the spectral theory of operators
matrices.
