Study On The Generalized Drazin Invertible Operators And Projection Operators

Firstly, we discuss the characterization of eigenprojections at zero of thegeneralized Drazin invertible operator on Banach space. By using the techniqueof block operator matrices, we extend the results that the characterization of eigen-projections at zero of matrices to operators in B(X). Furthermore , we discuss theperturbation of the generalized Drazin invertible operator. Finally, we study someproperties and characterizations of some special operators, i.e., projection opera-tors and EP operators. Utilizing the skills of operator matrix blocks, some prop-erties and characterizations of two commuting projection operators are presented.We also give some properties and characterizations of the EP operators based onthe eigenprojections and Moore-Penrose inverse.