On some subsets of Schechter's essential spectrum of a matrix operator and application to transport operator (Q2786303)

The primary goal of this paper is to investigate some essential spectra (essential approximate point spectrum, essential defect spectrum) of an operator that acts on a product of Banach spaces \(X\times Y\) and can be expressed as an operator matrix. In general, this type of operator is neither closed or closable, even if its entries are closed. The results obtained are applied to a two-group transport operator with general boundary conditions in the Banach space \(L_{p}([-a,a]\times[-1,1])\times L_{p}([-a,a]\times[-1,1])\), where \(a>0\) and \(p\geqslant 1\).