A NOTE ON THE REPRESENTATIONS FOR THE GENERALIZED DRAZIN INVERSE OF BLOCK MATRICES

摘要

We present some representations for the generalized Drazin inverse of a block matrix x =[abcd]in a Banach algebra A in terms of ad and（bc）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix.Also,several particular cases of this result are considered.