On deriving the generalized Drazin inverse of block matrices in a Banach algebra

摘要

This paper is devoted to the generalized Drazin inverse of a block matrix x = [a b c d] in a Banach algebra A, under specific conditions. We focus on deriving formulae for the generalized Drazin inverse of x in terms of the generalized Drazin inverses of the elements a, a bc, a(2)a(d) +aa(d) bca(d) and the generalized Schur complement s=d-ca(d) b.