Characterization of generalized essential spectra of 2 × 2 operator matrices via weakly demicompact operators
Mahamed Beghdadi, Bilel Krichen · Filomat · 2024
In this paper, we focus on the relationship between upper generalized semi-Fredholm and weakly demicompact operators acting on Banach spaces and we use this relation to extend some known results to generalized Fredholm theory. Moreover, in non-reflexive Banach spaces satisfying certain topo-logical properties, we develop under some conditions on its entries, generalized Fredholm results for a 2 ? 2 block operator matrix. The obtained results are used to characterize the generalized essential spectra, in particular the generalized Gustafson and Wolf essential spectra.