The Expression Of The Generalized Drazin Inverse Of A-CB

In this note, we mainly study the generalized Drazin inverse of A—CB over Ba-nach spaces stemd from the Drazin inverse and present its expressions under certain circumstance. The paper is organized as follows:In chapter 1, we give some required preparative knowledge including general sym-bols, definitions and basic lemmas.In chapter 2, we investigate the generalized Drazin inverse of A—CB over Banach spaces stemd from the Drazin inverse, and present its expressions under some conditions.In chapter 3, we disscuse some character to the core inverse of operator in the cor-ressponding to the point 0 eigenprojection, studies the relation to the two matrix of the same eigenprojection of the core inverse of operator and gives the pertubation of the core inverse in the case of the same eigenprojection.