Representations for the Drazin inverse of bounded operators on Banach space

Abstract

In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl.,
27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.