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| 摘要: |
| 本文研究了2×2无界对角算子矩阵在主对角扰动下的拟谱特性问题.首先,详细分析该矩阵在主对角扰动下的拟谱表现,对其进行了精细刻画.这一研究揭示了谱理论在拟谱情形下的复杂性,并构造具体例子说明了这一点.此外,利用内部元的信息进一步获得了四类拟点谱和两类拟剩余谱精细拟谱等式的结果,为拟谱的深入研究提供了参考. |
| 关键词: 无界算子矩阵|拟谱特性|拟点谱|拟剩余谱 |
| DOI： |
| 分类号:O177.1;O175.3 |
| 基金项目:国家自然科学基金(11861048)和内蒙古自然科学基金(2021MS01004)基金资助. |
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| UNBOUNDED DIAGONAL OPERATOR MATRIX’S PSEUDO-SPECTRAL EQUATION |
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WU Shu-zhen,HOU Guo-lin
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| Abstract: |
| This paper studies the quasi-spectrum characteristics of 2×2 unbounded diagonal operator matrices under the perturbation of the main diagonal. First, the pseudo-spectral behavior of the matrices under diagonal perturbations is analyzed in detail, and its pseudo-spectral properties are precisely described. This study reveals the complexity of pseudospectra and constructs speciflc examples to illustrate this point. In addition, by using the information of the internal element, the results of four types of quasi-point spectra and two types of quasi-residual spectra, as well as the detailed quasi-spectrum equalities, were further obtained., which provided a reference for further research on pseudo-spectra. |
| Key words: unbounded operator matrix|Pseudo-spectral properties|Pseudo-point spectrum|Pseudo-residual spectrum |
