A study of the properties of the gDMP inverse of an operator

Abstract

This paper investigates the gDMP inverse of generalized Drazin invert
ible operators with closed range. We introduce several characterizations
 and properties of the gDMP inverse, establish its generalized Drazin in
vertibility, and determine the conditions under which it is Moore–Penrose
 invertible. Key properties are derived, and applications to the solution of
 certain linear operator equations are also presented.