Generalized inverses of Bounded Finite Potent Operators on Hilbert Spaces

Abstract

The aim of this work is to prove the existence and uniqueness of the Drazin inverse and the DMP inverses of a bounded finite potent endomorphism. In particular, we give the main properties of these generalized inverses, we offer their relationships with the adjoint operator, we study their spectrum, we compute the respective traces and determinants and we relate the Drazin inverse of a bounded finite potent operator with classical definitions of this generalized inverse. Moreover, different properties of the Moore-Penrose inverse of a bounded operator are studied.