Formulas for the Drazin Inverse of Anti-Triangular Matrices

Let A be a Banach algebra. In this paper, for two Drazin invertible elements a; b ۲ A, explicit formulas for the Drazin inverse (a + b) are given in the cases of a۲ba = ۰, (ba)۲ = ۰ and ab۲ = ۰. By using these formulas, the representations for the Drazin inverse of the anti-triangular operator matrices over Banach algebras are obtained, which also extend some existing results.

کلیدواژه ها:

Banach algebra ، Block matrix ، Drazin inverse ، Index ، Operator matrix ، Schur complement