关于两个幂等算子组合的Drazin逆的若干探讨

Some discussions of the Drazin inverses of combinations of two idempotent operators

利用Hilbert空间上空间分解的技巧,讨论了两个幂等算子P,Q在条件PQP=0,PQP=P及PQP=PQ下的矩阵表示,探讨了组合aP+bQ+cPQ+dQP+eQPQ的Drazin逆的存在性,并且给出了Drazin逆的计算公式。

The matrix represenations of two idempotent operators P and Q under the conditions PQP = O, PQP = P and PQP = PQ are discussed respectively by using the technique of space decompositions of a Hilbert space. The existance and calculation formulas of Drazin inverse of the combinations aP ＋ bQ ＋ cPQ ＋ dQP ＋ eQPQ of the two idempotent operators are obtained.