Generalized Drazin Invertibility of Operator Matrices. (22nd November 2022)

• Record Type: Journal Article
• Authors: Bahloul, Aymen; Walha, Ines
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 16(2022)
• Page Start: 1836
• Page End: 1847
• Publication Date: 2022-11-22
• Subjects: Generalized Drazin invertibility -- generalized Drazin spectrum -- operator matrices -- single-valued extension property; 47A10 -- 47A11 -- 47B01; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2137811
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we investigate the generalized Drazin invertibility of upper triangular operator matrices acting on Banach spaces. Among other things, we explicit the defect set with respect to the local spectral theory. Moreover, we exhibit some sufficient conditions which assure that the generalized Drazin spectrum of a 3 × 3 upper triangular block operator matrix is the union of its diagonal entries spectra.