On relatively Fredholm perturbations and the stability of \(\textrm{M}\)-essential spectra associated with the sum of \(2\times 2\) block operator matrices

Abstract

In this paper, we develop a unified framework for studying the spectral stability of operator pencils whose entries satisfy relative Fredholm conditions. In particular, we derive new inclusion relations and stability criteria for the \(\textrm{M}\)-essential spectra of the sum of two unbounded \(2\times 2\) blocks operator matrix pencils.