| 上三角算子矩阵值域的闭性 |
| |
| 引用本文： | 杜贵春,邵春芳. 上三角算子矩阵值域的闭性[J]. 山东大学学报(理学版), 2012, 47(4): 42-46,52 |
| |
| 作者姓名： | 杜贵春 邵春芳 |
| |
| 作者单位： | 1. 安康学院数学系,陕西安康725000／武汉大学数学与统计学院,湖北武汉430072
2. 安康学院数学系,陕西安康,725000 |
| |
| 基金项目： | 安康学院2009年高层次人才专项项目(AYQDZR200913);陕西省教育厅科学研究项目(11JK043) |
| |
| 摘 要： | 设A∈B(H),B∈B(K),定义MC=(A C0B),其中C∈B(K,H)。基于算子分块的技巧,讨论了当R(A),R(B)都是闭的时候,对每一C∈B(K,H),R(MC)是闭的充要条件。进而研究了:(ⅰ)当R(A)不闭,R(B)闭时,以及当R(A)闭,R(B)不闭时,对任意C∈B(K,H),R(MC)不闭的充要条件;(ⅱ)当R(A),R(B)同时不闭时,对任意C∈B(K,H),R(MC)不闭的充要条件。
|
| 关 键 词： | 值域 算子矩阵 上三角算子矩阵 |
Closedness of ranges of upper triangular operator matrix |
| |
| DU Gui-chun,SHAO Chun-fang. Closedness of ranges of upper triangular operator matrix[J]. Journal of Shandong University, 2012, 47(4): 42-46,52 |
| |
| Authors: | DU Gui-chun SHAO Chun-fang |
| |
| Affiliation: | 1(1.Department of Mathematics,Ankang University,Ankang 725000,Shaanxi,China; 2.School of Mathematics and Statistics,Wuhan University,Wuhan 430072,Hubei,China) |
| |
| Abstract: | Let A∈B(H),B∈B(K).Defined the operator MC by MC=(A C0B),in which C∈B(K,H).Basing on the technique of block operator matrix,the sufficient and necessary conditions of the closedness of R(MC) for every C∈B(K,H) are discussed,when R(A) and R(B) are both closed.Furthermore,the following two questions are researched:(ⅰ) the sufficient and necessary conditions when the range R(MC) is not closed for every C∈B(K,H),when R(A) is not closed,R(B) is closed and the R(A) is closed,but R(B) is not closed;(ⅱ) the sufficient and necessary conditions when the range R(MC) is not closed for every C∈B(K,H),when both R(A) and R(B) are not closed. |
| |
| Keywords: | range operator matrix upper triangular operator matrix |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
