article: 1 from 1  
Publications de l'Institut Mathematique
2008, vol. 83, iss. 97, pp. 37-47
article language: English
unclassified
doi:10.2298/PIM0897037S
Drazin inverses of operators with rational resolvent
Schmoeger Christoph
Institut für Analysis, Universität, Karlsruhe, Germany

e-mail: christoph.schmoeger@math.uni-karlsruhe.de

Abstract

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.

Keywords

rational resolvent; Drazin inverse

References

KoBSON

Caradus, S.R. (1967) On meromorphic operators, I. Canad. J. Math, 19, 723-736

1

Caradus, S.R. (1974) Operator theory of the pseudo-inverse. Queen's papers in Pure and Appl. Math, br. 38

4

Heuser, H. (1986) Funktional analysis. Teubner

4

Taylor, A.E., Lay, D.C. (1980) Introduction to functional analysis. New York, itd: Wiley