Generalized inverses
This is a brief survey on generalized inverses of operators. The notions of inner and outer generalized inverses of bounded linear operators on Banach spaces, as well as the Moore-Penrose inverse of closed range bounded linear operators on Hilbert spaces, are presented using \(2 \times 2\) operator matrices. As an application, results on the reverse order law are proved. The existence of least squares solutions of linear equations is presented, as another application. The notion of Drazin inverse is posed in the setting of a complex unital Banach algebra, and by using properties of the spectrum and vector valued analytic functions, wherein operator matrices are replaced by the spectral idempotent. For the entire collection see [Zbl 1468.53002].
scientific article; zbMATH DE number 7391048