Spectral properties for generalized weakly S-demicompact operators. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Ferjani, Imen; Jeribi, Aref; Krichen, Bilel
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 4(2022)
• Page Start: 606
• Page End: 624
• Publication Date: 2022-03-04
• Subjects: Generalized weakly S-demicompact operator -- Fredholm and semi-Fredholm operators -- block operator matrix -- relative essential spectrum; 47A53 -- 47A10; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1737633
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this paper, we introduce the concept of generalized weakly S -demicompact operators with respect to a weakly closed linear operator S . We study the general setting of Fredholm theory. We give some perturbation results on the behaviour of relative essential spectra of the sum of two bounded linear operators by means of the relative essential spectra of each one. A characterization of generalized weakly S -demicompact operators by means of measures of weak noncompactness is given. Moreover, we impose some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak S -demicompactness of its closure.