线性算子的非负广义逆

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

线性算子的非负广义逆

宋显花()

青海师范大学数学与统计学院西宁 810016

收稿日期:2017-06-14 出版日期:2019-10-26 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

Xianhua Song()

College of Mathematics and Statistics, Qinghai Normal University, Xining 810016

Received:2017-06-14 Online:2019-10-26 Published:2019-11-08
Supported by:
the Qinghai Normal University School-Level Project: Generalized Inverse Study of Linear Operators(2018zr004)

摘要/Abstract

摘要：

设B（H）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A∈B（H）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 A∈ B(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

宋显花. 线性算子的非负广义逆[J]. 数学物理学报, 2019, 39(5): 1018-1024.

Xianhua Song. Nonnegative Generalized Inverses of Linear Operators[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1018-1024.

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