The drazin inverse for closed linear operators and the asymptotic convergence

摘要

The paper defines and studies the Drazin inverse for a closed linear operator A in a Banach space X in the case that 0 is an isolated spectral point of A. Results include an integral representation for the Drazin inverse of the infinitesimal generator of a C_0-semigroup and its application to a singular and singularly perturbed differential equation in a Banach space.