算子P+QP的数值域  

The numerical range of the operator P+QP

作　　者：张晨 余维燕[1] ZHANG Chen;YU Weiyan(College of Mathematics and Statistics,Hainan Normal University,Haikou 571158,Hainan,China)

机构地区：[1]海南师范大学数学与统计学院,海南海口571158

出　　处：《山东大学学报（理学版）》2023年第6期92-98,共7页Journal of Shandong University(Natural Science)

基　　金：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(120MS030,120QN250);海南省高等学校教育教学重点项目(hnjg2019ZD-13)。

摘　　要：本文研究了复可分Hilbert空间H上的两正交投影算子P和Q的组合P+QP的数值域。首先运用算子分块的方法给出了算子P+QP的数值域的支撑函数。然后运用支撑函数的性质给出了算子P+QP的数值域的一个几何刻画,即它的数值域闭包是参数在谱里的一些椭圆盘的闭凸包。In this paper,the numerical range of the combination P+QP of two orthogonal projections P and Q on a complex separable Hilbert space H is studied.Firstly,the support function of the numerical range of P+QP is given by using the method of operator block.Next,by using the properties of the support function,a 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.

关 键 词：数值域 支撑函数 正交投影 

分 类 号：O177.1[理学—数学]