您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (8): 39-44.doi: 10.6040/j.issn.1671-9352.0.2020.421

• • 上一篇    

幂等算子的左星序

郝宏艳,李愿*   

  1. 陕西师范大学数学与统计学院, 陕西 西安 710119
  • 发布日期:2021-08-09
  • 作者简介:郝宏艳(1996— ), 女, 硕士研究生, 研究方向为算子理论与量子信息. E-mail:1911753831@qq.com*通信作者简介:李愿(1977— ), 男, 教授, 博士生导师, 研究方向为算子理论及其应用. E-mail:yuanli@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11671242)

The left-star order for idempotent operators

HAO Hong-yan, LI Yuan*   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2021-08-09

PDF (PC)

204

摘要： 主要研究了Hilbert空间H上全体幂等算子关于左星序的性质, 其中左星序(left-star order)A*≤B定义为A*A=A*B且R(A)⊆R(B)。设A和B是幂等算子, 给出了A*≤B的等价条件和算子矩阵形式表示。同时, 当A*≤B时, 讨论了星序的上、下确界A∧B和A∨B的存在性及其表示。

关键词: 幂等算子, 左星序, 算子矩阵

Abstract: It is investigated that the characterizations of all idempotent operators on Hilbert space H with respect to the left-star order, which is defined by A*A=A*B and R(A)⊆R(B). Let A and B be two idempotent operators, the equivalent condition of A*≤B and the representation of operator matrix form is given. Meanwhile, the existence and representation of A∨B(supremum)and A∧B(infimum)of the star order when A*≤B is discussed.

Key words: idempotent operator, left-star order, operator matrix

中图分类号: 

  • O153.1
[1] DJIKIC M S, FONGI G, MAESTRIPIERI A. The minus order and range additivity[J]. Linear Algebra Appl, 2017, 531:234-256.
[2] DARZIN M P. Natural structures on semigroups with involution[J]. Bull Amer Math Soc, 1978, 84:139-141.
[3] LI Yuan, NIU Jiajia, XU Xiaoming. The minus order for idempotent operators[J/OL]. [2019-12-20]. Filomat. https://arxiv.org/abs/1912.09718.
[4] DENG Chunyuan, WANG Shunqin. On some characterizations of the partial orderings for bounded operators[J]. Math Ineq Appl, 2012(3):619-630.
[5] DENG Chunyuan, YU Anqi. Some relations of projection and star order in Hilbert space[J]. Linear Algebra Appl, 2015, 474:158-168.
[6] HARTWIG R E, DARZIN M P. Lattice properties of the star order for complex matrices[J]. J Math Anal Appl, 1982, 86:539-578.
[7] ANTEZANA J, CANO C, MOSCONI I, et al. A note on the star order in Hilbert spaces[J]. Linear and Multilinear Algebra, 2010, 58:1037-1051.
[8] XU Xiaoming, DU Hongke, LI Yuan, et al. The supremum of linear operators for the *-order[J]. Linear Algebra Appl, 2010, 433:2198-2207.
[9] LI Yuan, GAO Shuhui, XU Xiaoming. The star order for idempotent operators[J/OL]. [2021-02-14]. Linear and Multilinear Algebra. https://doi.org/10.1080/03081087.2021.1887069.
[10] DOLINAR G, MAROVT J. Star partial order on B(H)[J]. Linear Algebra Appl, 2011, 434:319-326.
[11] MITRA S K. The minus partial order and the shorted matrix[J]. Linear Algebra Appl, 1986, 83:1-27.
[12] C(-overL)RULIS J. One-sided star partial orders for bounded linear operators[J]. Operators and Matrices, 2015(9):891-905.
[13] BAKSALARY J K, BAKSALARY O M, LIU Xiaoji. Further properties of the star, left-star, rightstar, and minus partial orderings[J]. Linear Algebra Appl, 2003, 375:83-94.
[1] 杨源, 张建华. B(H)上中心化子的一个局部特征[J]. 山东大学学报（理学版）, 2015, 50(12): 1-4.
[2] 陈一鸣, 柯小红, 韩小宁, 孙艳楠, 刘立卿. 小波法求解分数阶微分方程组及其收敛性分析[J]. 山东大学学报（理学版）, 2015, 50(02): 67-74.
[3] 谢涛,左可正. 关于两个幂等算子组合的Drazin逆的若干探讨[J]. J4, 2013, 48(4): 95-103.
[4] 耿万海,陈一鸣,刘玉风,汪晓娟. 应用Haar小波和算子矩阵求定积分的近似值[J]. J4, 2012, 47(4): 84-88.
[5] 杜贵春1,2,邵春芳1. 上三角算子矩阵值域的闭性[J]. J4, 2012, 47(4): 42-46.
[6] 段樱桃. 两个算子乘积的｛1,3,4｝逆序律[J]. J4, 2012, 47(4): 53-56.
[7] 许俊莲1,2. 算子方程 AXB*-BX*A*=C的解[J]. J4, 2012, 47(4): 47-52.
[8] 许俊莲. 几个正交投影函数的特征值函数[J]. J4, 2011, 46(6): 70-74.
[9] 方莉1,白维祖2. 保持幂等算子乘积或约当三乘积非零幂等性的映射[J]. J4, 2010, 45(12): 98-105.
[10] 李 愿 . 2×2上三角算子矩阵的Weyl定理[J]. J4, 2007, 42(6): 69-73 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发