# Journal of Operator Theory

Volume 46, Issue 2, Fall 2001 pp. 323-336.

The Drazin inverse for closed linear operators and the asymptotic Conve rgence of $C_0$-semigroups**Authors**: J.J. Koliha (1), and Trung Dinh Tran (2)

**Author institution:**(1) Dept. of Mathematics and Statistics, University of Melbourn, VIC 3010, Australia

(2) Dept. of Mathematics and Statistics, University of Melbourn, VIC 3010, Australia

**Summary:**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 \Csem\ and its application to a singular and singularly perturbed differential equation in a Banach space.

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