算子矩阵值域的闭性及其应用  

Closedness of Ranges for Operator Matrices and Its Application

作　　者：董炯[1,2] 曹小红[2] DONG Jiong;CAO Xiaohong(Department of Mathematics,Changzhi University,Changzhi 046011,Shanxi,China;School of Mathematics and Information Science,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]长治学院数学系,山西长治046011 [2]陕西师范大学数学与信息科学学院,西安710119

出　　处：《数学年刊（A辑）》2020年第4期383-398,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11471200,No.11701351);陕西省自然科学基础研究(No.2018JQ1082)的资助。

摘　　要：令H和K均为无限复可分的Hilbert空间.定义M_(X)=(A C X B)为作用在H⊕K上的2×2算子矩阵,其中X为从H到K上未知的有界线性算子.在本文中,基于R(C)的闭性对某个(或任意的)X∈B(H,K),使得R(M_(X))为闭集的充要条件做了等价刻画.另外,研究了算子矩阵M_(X)的半Fredholm性与广义Weyl性并给出了一些相应的结论.Let H and K be infinite dimensional separable complex Hilbert spaces.The authors denote byM_(X)=(A C X B)a 2×2 operator matrix acting on H⊕K,where X is an unknown bounded linear operator from H to K.In this paper,based on the closedness of R(C),the authors characterize the necessary and sufficient condition for R(M_(X))to be closed for some(or every)X∈B(H,K).In addition,the authors study the semi-Fredholmness and generalized Weylness of M_(X)and give some relevant results.

关 键 词：值域 半FREDHOLM算子 算子矩阵 广义Weyl算子 

分 类 号：O177.1[理学—数学]