The Drazin inverses of Combinations of Two idempotents
Tao Xie, Kezheng Zuo · European Journal of Pure and Applied Mathematics · 2012
By using the methods of splitting operator's matrix into blocks and space decompositions, the existence and calculation formulas of Drazin inverse of the combinations aP+bQ+cPQ of two idempotent operators P and Q on a Hilbert space are obtained under the conditions PQP=0,PQP=P and PQP=PQ respectively.These generalized the related results of Deng's work, which characterized the Drazin inverse of the sum and difference of two idempotents.