Characterization of generalized essential spectra of 2 × 2 operator matrices via weakly demicompact operators
Abstract
The purpose of this research paper is to describe the generalized essential
spectra of operator matrices. First, we give the relationship between upper generalized semi-Fredholm and weakly demicompact operators in Banach spaces. Also, using this relation, we investigate some generalized Fredholm results for a 2 × 2 operator matrices, in non-reflexive Banach spaces that satisfy certain properties, which that its entries have some conditions. Finally, we use the obtained results to characterize the generalized essential spectra of a 2 × 2 operator matrices.
spectra of operator matrices. First, we give the relationship between upper generalized semi-Fredholm and weakly demicompact operators in Banach spaces. Also, using this relation, we investigate some generalized Fredholm results for a 2 × 2 operator matrices, in non-reflexive Banach spaces that satisfy certain properties, which that its entries have some conditions. Finally, we use the obtained results to characterize the generalized essential spectra of a 2 × 2 operator matrices.
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