Weighted G-Outer Inverse of Banach Spaces Operators. (23rd May 2022)

• Record Type: Journal Article
• Authors: Mosić, Dijana
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 5(2022)
• Page Start: 558
• Page End: 579
• Publication Date: 2022-05-23
• Subjects: G-outer inverse -- G-outer partial order -- W-weighted outer inverse -- W-weighted G-Drazin inverse; 47A05 -- 47A62 -- 15A09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2051186
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In order to extend the notions of G-outer inverses and weighted G-Drazin inverses, we firstly define and characterize the ( M, N )-weighted outer inverses for Banach spaces operators. Using the ( M, N )-weighted outer inverse, beside the ( M, N )-weighted outer equivalence relation, we create and study the ( M, N )-weighted G-outer inverse of an operator between two Banach spaces. This new inverse presents generalization of the G-outer inverse and the W -weighted G-Drazin inverse. By means of ( M, N )-weighted G-outer inverse, we also introduce and investigate the ( M, N )-weighted G-outer relation which is a preorder on corresponding set. Thus, we extend the notions of the G-outer partial order and the W -weighted G-Drazin preorder for Banach spaces operators.