数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1018-1024.

• 论文 • 上一篇    

线性算子的非负广义逆

宋显花   

  1. 青海师范大学数学与统计学院 西宁 810016
  • 收稿日期:2017-06-14 修回日期:2019-01-18 发布日期:2019-11-08
  • 作者简介:宋显花,E-mail:735877306@qq.com
  • 基金资助:
    青海师范大学校级项目:线性算子的广义逆研究(2018zr004)

Nonnegative Generalized Inverses of Linear Operators

Song Xianhua   

  1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810016
  • Received:2017-06-14 Revised:2019-01-18 Published:2019-11-08
  • Supported by:
    Supported by the Qinghai Normal University School-Level Project:Generalized Inverse Study of Linear Operators (2018zr004)

摘要: BH)是复Hilbert空间H上有界线性算子全体组成的集合.该文主要利用算子分块技巧给出闭值域算子ABH)的非负{1,3}-逆,{1,4}-逆,{1,3,4}-逆存在的充要条件以及它们的一般形式.同时,该文也得到A的非负{1,3}-逆存在与非负{1,2,3}-逆存在是等价的,非负{1,4}-逆存在与非负{1,2,4}-逆存在是等价的.

关键词: 非负广义逆, Moore-Penrose逆, 正算子

Abstract: Let B(H) be the set of all bounded linear operators on a complex Hilbert space H. Using the block operator technique, some necessary and suffcient conditions for the existence of nonnegative {1, 3}-, {1, 4}-, {1, 3, 4}-inverses for an operator AB(H) with closed range is given in this paper, and these sets are completely descibed. Moreover, it is showed that the existence of nonnegative {1, 3}-, {1, 4}-inverse of an operator A is equivalent to existence of its nonnegative {1, 2, 3}-, {1, 2, 4}-inverse, respectively.

Key words: Nonnegative generalized inverse, Moore-Penrose inverse, Positive operator

中图分类号: 

  • O177.1