算子AB值域的闭性  

The closeness of range of operator AB

作　　者：许俊莲[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2012年第1期30-31,35,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：宝鸡文理学院重点科研项目(ZK11132)

摘　　要：目的在算子A,B值域闭的条件下,讨论2个算子的乘积AB值域闭的充要条件,其中A,B是作用在Hilbert空间H上的有界线性算子。方法利用算子分块的技巧。结果与结论得出了AB值域闭的3个充要条件,并给出了证明。Aim To discuss the sufficient and necessary conditions for the closed range of operator AB when the ranges of operators A and B are closed, and operators A and B are bounded linear operators on a Hilbert space H. Methods The technique of block operator matrix is used. Result and Conclusion Three sufficient and necessary conditions for the closed range of operator AB are obtained and the proofs are given.

关 键 词：值域 MOORE-PENROSE逆 算子矩阵 正交投影 

分 类 号：O177.1[理学—数学]