On the Characterization of Finite Potent Endomorphisms via their Finite Potent 1-inverses and a Generalization of the Minus Partial Order

Abstract The main theorem that is proven in this article is that two finite potent endomorphisms are equal if and only if their respective sets of finite potent 1-inverses coincide. In order to do this, there are several results dealing with generalized inverses on infinite dimensional vector spaces that are offered. As an application of the previous result, the theory for the minus partial order of finite potent endomorphisms is developed, which generalizes the theory of the minus partial order for finite square matrices.