Abstract
Let A be a complex Banach algebra with unit and let p,q be two idempotents in A. For α,β∈C\\{0}, the authors obtain an explicit representation formula for the Drazin inverse of αp+βq and give the upper bound of the corresponding Drazin index by using the presented method. As a consequence, the main previously published results on Drazin inverse of αp+βq are corollaries of our theorem. Finally, the authors apply the theorem to an example which cannot be solved by previously known results.
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