两正交投影组合的Moore-Penrose逆的数值域

doi:10.6040/j.issn.1671-9352.0.2023.383

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 100-106.doi: 10.6040/j.issn.1671-9352.0.2023.383

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两正交投影组合的Moore-Penrose逆的数值域

王然,余维燕^*

海南师范大学数学与统计学院, 海南海口 571158

发布日期:2025-05-19
通讯作者: 余维燕(1969— ),女,教授,博士生导师,博士,研究方向为算子代数. E-mail:wyyume65@163.com
作者简介:王然(2000— ),女,硕士研究生,研究方向为算子理论与算子代数. E-mail:2158842933@qq.com*通信作者:余维燕(1969— ),女,教授,博士生导师,博士,研究方向为算子代数. E-mail:wyyume65@163.com
基金资助:
国家自然科学基金资助项目(12061031,11461018);海南省自然科学基金资助项目(120MS030,123RC473)

Numerical range of Moore-Penrose inverses of a combination of two orthogonal projections

WANG Ran, YU Weiyan^*

College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, Hainan, China

Published:2025-05-19

摘要/Abstract

摘要： 设H为一个复可分Hilbert空间,P和Q为H上的2个正交投影算子。研究P和Q的组合P+QP的Moore-Penrose逆算子(P+QP)^†的数值域,运用算子分块技巧给出算子(P+QP)^†的数值域的几何刻画,即它的数值域闭包是参数在算子PQ谱里的一些椭圆的闭凸包。

关键词: 数值域, 正交投影, Moore-Penrose逆, 支撑函数

Abstract: Let H be a complex separable Hilbert space, and P and Q be two orthogonal projection operators on H. This article mainly studies the numerical range of the Moore-Penrose inverse operator(P+QP)^† of the combination of P and Q. By using the operator block technique, the geometric characterization of the numerical range of the operator(P+QP)^† is given. That is, the closure of its numerical range is a closed convex hull of some explicit ellipses parameterized by points in the spectrum of operator PQ.

Key words: numerical range, orthogonal projections, Moore-Penrose inverse, support function

中图分类号:

O177.1

王然,余维燕. 两正交投影组合的Moore-Penrose逆的数值域[J]. 《山东大学学报(理学版)》, 2025, 60(5): 100-106.

WANG Ran, YU Weiyan. Numerical range of Moore-Penrose inverses of a combination of two orthogonal projections[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 100-106.

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两正交投影组合的Moore-Penrose逆的数值域

Numerical range of Moore-Penrose inverses of a combination of two orthogonal projections

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