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The g-Drazin inverse involving power commutativity

The g-Drazin inverse involving power commutativity

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 ? A qnil. Let a, b ? Ad. If a3b = ba, b3a = ab, and a2adb = aadba, we …