More results on generalized Drazin inverse of block matrices in Banach algebras

In a Banach algebra A, let x = [(ab)(cd)] is an element of A relative to the idempotent p is an element of A, where a is an element of pAp is generalized Drazin invertible. Under assumptions that the generalized Schur complement s = d-ca(d)b is an element of (1 - p)A(1 - p) and the element ca(pi) is an element of (1 - p)A(1 - p) are generalized Drazin invertible, we establish some formulae for the generalized Drazin inverse of x in terms of a matrix in the generalized Banachiewicz-Schur form and its powers. We develop necessary and sufficient conditions for the existence and the expressions for the group inverse of a block matrix in Banach algebras. The provided results extend earlier works given in the literature. (C) 2013 Elsevier Inc. All rights reserved.