The representation of the Drazin inverse of anti-triangular operator matrices based on resolvent expansions

Keywords: Drazin inverse Anti-triangular operator matrix Resolvent expansion a b s t r a c t This paper deals with the anti-triangular operator matrix M ¼ A B C 0 with A 2 ¼ A and CA p B ¼ 0. Using the resolvent expansion technique, we obtain the explicit representation of the Drazin inverse of M, in terms of its entries and the Drazin inverses of the entries and their compositions. The result extends the main results in Bu et al.