| 李佳丽,吴秀峰,阿拉坦仓.3×3上三角关系矩阵的闭值域谱的扰动[J].数学年刊A辑,2024,45(4):357~372 |
| 3×3上三角关系矩阵的闭值域谱的扰动 |
| Perturbation of Closed Range Spectra for 3 × 3 Upper Triangular Relation Matrices |
| Received:April 15, 2024 Revised:November 08, 2024 |
| DOI：10.16205/j.cnki.cama.2024.0025 |
| 中文关键词: 关系矩阵 值域的闭性 闭值域谱 扰动 |
| 英文关键词:Relation matrix, Closedness of range, Closed range spectrum,
Perturbation |
| 基金项目:内蒙古自治区自然科学基金项目(No.2022LHMS01003)； 内蒙古自治区高等学校青年科技英才项目(No.NJYT22029)； 内蒙古师范大学基本科研业务费专项资金资助项目(No.2022JBBJ009)； 内蒙古自治区一流学科科研专项项目(No.YLXKZX-NSD-011,No.YLXKZX-NSD-001) |
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| 中文摘要: |
| 设H1,H2,H3为无穷维复可分Hilbert空间.对给定关系A∈LR（H1）,B∈LR（H2）,C∈LR（H3）,记3×3上三角关系矩阵为MD,E,F:=■.作者借助对角关系A,B,C的谱性质,给出了对任意的D∈B（H2,H1）,E∈B（H3,H1）,F∈B（H3,H2）,使得MD,E,F都有值域不闭的充分必要条件,并进一步刻画了MD,E,F的闭值域谱的扰动. |
| 英文摘要: |
| Let H1, H2 and H3 be complex separable infinite-dimensional Hilbert spaces.
Given the relations A ∈ LR(H1), B ∈ LR(H2) and C ∈ LR(H3), the authors define
MD,E,F := A D E 0 0 0 B F C . In this paper, a necessary and sufficient condition is given for the range
of MD,E,F is not closed for any D ∈ B(H2, H1), E ∈ B(H3, H1) and F ∈ B(H3, H2), in terms
of the spectral properties of diagonal relations of A, B and C in MD,E,F. Furthermore, the
authors characterize the perturbation of closed range spectrum of MD,E,F. |
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