幂等算子核空间上的投影  

The Projection on the Kernel Space of Idempotent Operator

作　　者：刘妮 任谨慎 冯军庆[1] 郑芳 LIU Ni;REN Jin-shen;FENG Jun-qing;ZHENG Fang(Department of Basic,Air Force Engineering University,Xi’an 710051,China)

机构地区：[1]空军工程大学基础部,西安710051

出　　处：《西安文理学院学报（自然科学版）》2023年第1期1-3,共3页Journal of Xi’an University(Natural Science Edition)

基　　金：陕西省自然科学面上基金项目(2019JM252)。

摘　　要：记H为复可分无限维Hilbert空间,H上的有界线性算子F若满足F^(2)=F,则称F为幂等算子,P_((N(F))),P_(F)分别为幂等算子F的核空间N(F),值域R(F)上正交投影.借助算子分块技巧,给出P_(F)P_((N(F)))范数的表达式,进一步研究了P_(Q)P_((N(Q)))及P_(Q)-P_((N(Q)))范数的最大值与最小值,其中Q是满足R(Q)=R(F)的H上的幂等算子.Let H be a complex separable infinite dimensional Hilbert space.If the bounded linear operator F on H satisfies F^(2)=F,then F is called an idempotent operator.P_(N(F))and P_(F)are respectively the orthogonal projections on the kernel space N(F)and the range R(F)of the idempotent operator F.The expression of norm P_(F)P_(N(F))is given by means of operator partition technique,and the maximum and minimum values of norm P_(Q)P_(N(Q))and norm P_(Q)-P_(N(Q))are further studied,where Q is an idempotent operator on H satisfying R(Q)=R(F).

关 键 词：HILBERT空间 幂等算子 核空间 正交投影 

分 类 号：O177.1[理学—数学]