On the Drazin inverse of the linear combinations of two idempotents in a complex Banach algebra.

Abstract: Let be a complex Banach algebra with unit and let be two idempotents in . For , the authors obtain an explicit representation formula for the Drazin inverse of 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 are corollaries of our theorem. Finally, the authors apply the theorem to an example which cannot be solved by previously known results. [Copyright &y& Elsevier]