Communications of the
Korean Mathematical Society CKMS

Measure of non strict cosingularity appears as one of the most particular class of Fredholm perturbation allowing to draft an interesting use in the analysis of spectral properties of linear operators in particular operator matrix field. The main purpose of this paper is to establish some new stability results of perturbed lower semi-Fredholm (semi-Weyl) operators linked to the use of measure of non strict cosingularity and the theory of Fredholm inverse. Moreover, we apply our results in order to investigate a new framework of the characterization of some essential spectra of unbounded block $3\times 3$ operator matrix with maximal domain.

Keywords: Measure of non strict cosingularity, theory of Fredholm operators, operators theory, theory of operator matrices, essential spectra

MSC numbers: Primary 47A56, 47A13, 47A53, 47A10, 47A55