Explicit formulae for the generalized Drazin inverse of block matrices over a Banach algebra

Abstract

    In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a $2\times2$ block matrix in a Banach algebra under weaker restrictions. Our results generalize and unify several results in the literature.