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

In a Banach algebra A, let x=[abcd]∈A relative to the idempotent p∈A, where a∈pAp is generalized Drazin invertible. Under assumptions that the generalized Schur complement s=d−cadb∈(1−p)A(1−p) and the element caπb∈(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.