Djordjević, D. S.; Stanimirović, P. S.; Wei, Y. The representation and approximations of outer generalized inverses. (English) Zbl 1071.65075 Acta Math. Hung. 104, No. 1-2, 1-26 (2004). Let \(X\) and \(Y\) be Banach spaces, and \(A\in L(X,Y)\). An operator \(G\in L(X,Y)\) is called an outer generalized inverse \((OGI)\) of \(A\) if \(GAG=G\). A unified representation theorem for the class of all \(OGI\)’s of an operator is presented. The theorem is a generalization for the corresponding representation of the Moore-Penrose inverse [see C. W. Groetsch, J. Math. Anal. Appl. 49, 154-157(1975; Zbl 0295.47012)], of the Drazin inverse [see Y. Wei and S. Qiao, Appl. Math. Comput. 138, 77-89 (2003; Zbl 1034.65037)], and of the specific generalized inverse studied by Y. Wei [Linear Algebra Appl. 280, 87-96 (1998; Zbl 0934.15003)]. The unified representation is used to develop several particular expressions and computational procedures for the set of \(OGI\)’s. Some illustrative numerical examples are given. Reviewer: Oleksandr Kukush (Kiev) Cited in 42 Documents MSC: 65J10 Numerical solutions to equations with linear operators 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Keywords:outer generalized inverses; representation; Banach spaces; Moore-Penrose inverse; Drazin inverse; numerical examples Citations:Zbl 0295.47012; Zbl 1034.65037; Zbl 0934.15003 PDFBibTeX XMLCite \textit{D. S. Djordjević} et al., Acta Math. Hung. 104, No. 1--2, 1--26 (2004; Zbl 1071.65075) Full Text: DOI