Stability of Schechter essential spectrum of 2×2 block operator matrix by means of measure of non strict singularity and application

In this paper, we give some new results on the spectral theory for some operator matrices. It focuses on the theory of the measure of non strict singularity which amounts to study the stability of the Schechter essential spectrum of unbounded block 2×2 operator matrix in terms of the union of the Schechter essential spectrum of its diagonal operators entries. This result is tested for two-group transport operator model.