Geodesic
Drazin Inverses of Operators With Rational Resolvent
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 37 .

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Let $A$ be a bounded linear operator on a Banach space such that the resolvent of $A$ is rational. If $0$ is in the spectrum of $A$, then it is well known that $A$ is Drazin invertible. We investigate spectral properties of the Drazin inverse of $A$. For example we show that the Drazin inverse of $A$ is a polynomial in $A$.
DOI : 10.2298/PIM0897037S
Classification : 47A10
Keywords: rational resolvent, Drazin inverse 
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     author = {Christoph Schmoeger},
     title = {Drazin {Inverses} of {Operators} {With} {Rational} {Resolvent}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {37 },
     publisher = {mathdoc},
     volume = {_N_S_83},
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     year = {2008},
     doi = {10.2298/PIM0897037S},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897037S/}
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Christoph Schmoeger. Drazin Inverses of Operators With Rational Resolvent. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 37 . doi : 10.2298/PIM0897037S. http://geodesic.mathdoc.fr/articles/10.2298/PIM0897037S/

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