Let A be a complex Banach algebra. An element a ∈ A has g-Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a − a2b ∈ Aqnil . Let a, b ∈ Ad . If a3b = ba, b3a = ab, and a2adb = aadba, we prove that a + b ∈ ...