Outer generalized inverses with prescribed ideals
Gabriel Kantún-Montiel · Linear and Multilinear Algebra · 2013
The outer inverse of a bounded linear operator on a Banach space is unique if we fix its range and nullspace. In this note we review several approaches to the uniqueness of the outer inverse in rings and explore the underlying idea of prescribing certain ideals in a way that mimics the operators case. Starting with Djordjevic and Wei -inverses, we show some connections with Mary’s inverse along an element and give a characterization of Drazin’s annihilator -inverse.