Left and Right Generalized Drazin Invertibility of an Upper Triangular Operator Matrices with Application to Boundary Value Problems

Abstract

In this paper we investigate the quasi-nilpotent part and the analytical core for the upper triangular operator matrix M C in terms of those of A and B. We give some necessary and sufficient conditions for M C to be left or right generalized Drazin invertible operator for some C ∈ B(K, H). As an application, we study the existence and uniqueness of the solution for abstract boundary value problems described by upper triangular operator matrices with right generalized Drazin invertible component.