On the generalized Drazin-Riesz inverse for closed linear operators
Let \(X\) be a complex Banach space, \(B(X)\) stand for the space of bounded linear operators, and \(C(X)\) denote the space of closed linear operators, on \(X\), respectively. Let \(R(.)\) and \(D(.)\) denote the range space and the domain space, respectively. \(A \in C(X)\) is said to be generalized Drazin-Riesz invertible if there exists \(B\in B(X)\) such that the following are satisfied: \(R(B) \subseteq D(A)\), \(R(I-AB) \subseteq D(A)\), \(AB=BA\), \(BAB=B\), and the operator \(A(I-AB)\) is bounded Riesz. In this paper, some of the basic results on Drazin invertibility of bounded operators are extended to closed linear operators.
scientific article; zbMATH DE number 7465522
scientific article