Аннотация:Abstract The generalized Drazin inverse M d of a 2 × 2 operator matrix is considered, where A ∈ ℬ(X) and D ∈ ℬ(Y) are generalized Drazin invertible. Expressions for the generalized Drazin inverse M d of operator matrix M in terms of the individual blocks A, B, C, D, A d and D d are derived under some conditions. Keywords: generalized Drazin inverseSchur complementblock matrixAMS Subject Classifications:: 15A0947A05 Acknowledgements The authors would like to thank our editor Prof. Fuzhen Zhang and two referees for their very detailed comments which greatly improved our presentation. Partial support for C. Deng was provided by the National Natural Science Foundation Grants of China (No. 10571113). The work of D.S. Cvetković-Ilić was supported by Grant No. 144003 of the Ministry of Science, Technology and Development, Republic of Serbia. The work of Y. Wei was supported by the National Natural Science Foundation of China under grant 10871051 and Shanghai Science and Technology Committee under grant 08DZ2271900.
