【摘要】 讨论了Hilbert空间上的两个不同的幂等算子P、Q的组合aP+bQ-cPQ的Drazin可逆性问题,利用幂等算子的性质和空间分解的技巧证明了aP+bQ-cPQ的Drazin逆在条件PQP=0下是存在的,并且给出了其逆的计算公式,其中a,b,c∈C,ab≠0.更多还原

【Abstract】 Discussed the problem of Drazin invertibility of combinations of two idempotent operators P、Q on a Hilbert space.By using the properties of idempotent operators and the techniques of space decomposition,prove the existance of Drazin invertibility of the combinations aP + bQ-cPQ and its expression is also obtained,where a,b,c∈C,ab≠0.更多还原