W-weighted Drazin Inverse Of Linear Combination Of The Orthogonal Projection And Idempotent

By using space decomposition, we demonstrate the linear combination of the orthog-onal projection and idempotent operator on the Hilbert space is to be W-weighted Drazin inverse under the conditions (1) PQP=P, (2) PQP=0, (3) PQP=PQ, and its repre-sentations are given. Furthermore, some concrete examples are constructed to illustrate the effectiveness of our results.