Abstract
We present necessary and sufficient conditions under which the anti-triangular matrix (a b 1 0) over a Banach algebra has g-Drazin inverse. New additive results for g-Drazin inverse are obtained. Then we apply our results to 2 ? 2 operator matrices and generalize many known results, e.g., [5, Theorem 2.2], [13, Theorem 2.1] and [14, Theorem 4.1].
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