Pseudo-Generalized Inverse and Drazin Invertibility

摘要

This work deals with some generalizations of the Drazin invertibility, involving the pseudo-generalized invertibility that has been studied recently by the authors in Lahmar and Skhiri (Filomat 36:2551-2572, 2022) and Lahmar and Skhiri (Filomat 36:4575-4590, 2022). We also introduce a new notion of DPG inverse and the relationships between the notions of DPG inverse, Drazin inverse and EP operator, are studied in this paper. An application of DPG inverses to some operator equations is also provided.