The representation and approximations of outer generalized inverses

Abstract

We present a unified representation theorem for the class of all outer generalized inverses of a bounded linear operator. Using this representation we develop a few specific expressions and computational procedures for the set of outer generalized inverses. The obtained result is a generalization of the well-known representation theorem of the Moore--Penrose inverse as well as a generalization of the well-known results for the Drazin inverse and the generalized inverse AT,S (2). Also, as corollaries we get corresponding results for reflexive generalized inverses.