中文摘要：

本文采用预解式的Laurent展开方法讨论了两个有界线性算子和的Drazin可逆性及其表达式.在P3=0,PQ2=0,PQP2 Q=0的条件下,证明了P＋Q是Drazin可逆的,并得到了P＋Q的Drazin逆的表达式.最后,给出数值算例说明结论的有效性.

英文摘要：

In this paper,we discuss the existence and the representation of the Drazin inverse of the sum for two bounded linear operators by using the Laurent expansion of resolvent on a Banach space. Under the assumptions p3 = 0, pQ2 = 0, proved,At the same time,we obtain the given to illustrate its effectiveness. pQp2Q =0, the existence of the Drazin inverse of P ＋ Q is representation of （P ＋ Q）9. Finally, a numerical example is