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| 摘要: |
| 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. 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给出了四类拟点谱和两类拟剩余谱精细的拟谱等式, 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:O175. 3 |
| 基金项目: |
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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: |
| The pseudo-spectral characteristics of the 2×2 unbounded diagonal operator matrices are studied in diagonal perturbations. 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 specific examples to illustrate this point. In addition, using information about internal elements, the fine spectral equalities of four classes of pseudo-point spectra and two classes of pseudo-residual spectra are given, which provide a reference for further research on pseudo-spectra. |
| Key words: unbounded operator matrix Pseudo-spectral properties Pseudo-point spectrum Pseudo-residual spectrum |
