有界线性算子乘积的Drazin可逆性及其Drazin逆的逆序律  

Drazin invertibility of product and reverse order law of Drazin inverse for bounded linear operators

作　　者：仲程程 王华[1] Zhong Chengcheng;Wang Hua(College of Sciences,Inner Mongolia University of Technology,Huhhot 010051,China)

机构地区：[1]内蒙古工业大学理学院数学系,内蒙古呼和浩特010051

出　　处：《纯粹数学与应用数学》2020年第3期368-378,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11461049,11601249);内蒙古自然科学基金(2018MS01002,2017MS0118).

摘　　要：讨论了有界线性算子乘积的Drazin可逆性及逆序律成立的充要条件.具体地,给出了三个有界线性算子在具有交换条件[P;PQ]=0和[P,Q,R]=0下其乘积的Drazin可逆性以及Drazin逆的逆序律成立的充要条件;讨论了两个有界线性算子在交换条件[P,P^2Q]=0和Q[P,PQ]=0下乘积的Drazin可逆性以及Drazin逆的逆序律成立的充要条件.In this paper,we discuss the Drazin invertibility of product and the sufficient and necessary conditions of the reverse order laws to hold for the Drazin inverse of bounded linear operators.Concretely,firstly,we discuss the Drazin invertibility of the product of three bounded linear operators under commutation conditions[P,PQ]=0 and[P,Q,R]=0,and obtain the sufficient and necessary conditions for the reverse order law of Drazin inverse(PQR)D=R^DQ^DP^D to hold.Secondly,we discuss the Drazin invertibility of the product of two bounded linear operators under commutation conditions[P,P^2Q]=0 and Q[P,PQ]=0,and obtain the sufficient and necessary conditions for the reverse order law of Drazin inverse(PQ)D=QDPD to hold.

关 键 词：DRAZIN逆 逆序律 空间分解 有界线性算子 

分 类 号：O151.21[理学—数学] O177.2[理学—基础数学]