| 摘要: |
| 本文首先证明了有界线性算子在任意微小有界算子扰动下, 值域闭性的稳定性, 并且探讨了拟近似点谱与拟亏谱的共轭性. 其次, 本文探讨了上三角型扰动下的~$2\times2$~上三角分块算子矩阵的拟近似点谱、拟亏谱与其对角元的拟近似点谱、拟亏谱之间的包含关系与等价描述. 最后, 本文研究了上三角分块算子矩阵在上三角有界扰动情形下的精细拟谱. |
| 关键词: 算子矩阵 拟谱 拟点谱 拟近似拟谱 拟亏谱 |
| DOI： |
| 分类号:O175.3; O177.7 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目）；包头师范学院高层次人才引进科研启动基金(BTTCRCQD2025-204)资助 |
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| THE FINE CHARACTERIZATION OF PSEUDO-SPECTRA FOR UPPER-TRIANGULAR BLOCK OPERATOR MATRICES |
|
shenrunshuan
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| Abstract: |
| This paper first proves the stability of the closedness of the range for bounded linear operators under arbitrary infinitesimal bounded perturbations, and explores the conjugacy between the pseudo-approximate point spectrum and the pseudo-defect spectrum. Secondly, it investigates the inclusion relations and equivalent descriptions between the pseudo-approximate point spectrum and pseudo-defect spectrum of $2\times2$~upper triangular block operator matrices under upper triangular perturbations and those of their diagonal entries. Finally, the paper studies the fine pseudo-spectra of upper triangular block operator matrices under bounded upper triangular perturbations. |
| Key words: operator matrices pseudo-spectrum pseudo-point spectrum pseudo-approximate point spectrum pseudo-defect spectrum. |
