| 3×3阶上三角算子矩阵的点谱、剩余谱和连续谱 |
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| 引用本文： | 吴秀峰,黄俊杰.3×3阶上三角算子矩阵的点谱、剩余谱和连续谱[J].数学学报,2019,62(6):817-832. |
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| 作者姓名： | 吴秀峰 黄俊杰 |
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| 作者单位： | 内蒙古师范大学 数学科学学院 呼和浩特 010022 |
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| 基金项目： | 国家自然科学基金项目（11761052）；内蒙古自治区自然科学基金（2018BS01001）；内蒙古自治区高等学校科学研究重点项目（NJZZ18018）；内蒙古师范大学引进人才项目（2017YJRC018） |
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| 摘 要： | 记■为Hilbert空间■上的上三角算子矩阵.我们借助对角元A,B和C的谱性质给出了σ_*(M_(D,E,F))=σ_*(A)∪σ_*(B)∪σ_*(C)对任意D∈B(H_2,H_1),E∈B(H_3,H_1),F∈B(H_3,H_2)均成立的充要条件,其中σ_*代表某类特定的谱,如点谱、剩余谱和连续谱等.此外,给出了一些例证.
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| 关 键 词： | 点谱 剩余谱 连续谱 3×3阶上三角算子矩阵 |
The Point,Residual and Continuous Spectrum of 3×3 Upper Triangular Operator Matrices |
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| Xiu Feng WU,Jun Jie HUANG.The Point,Residual and Continuous Spectrum of 3×3 Upper Triangular Operator Matrices[J].Acta Mathematica Sinica,2019,62(6):817-832. |
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| Authors: | Xiu Feng WU Jun Jie HUANG |
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| Institution: | School of Mathematical Science, Inner Monogolia Normal University, Hohhot 010022, P. R. China |
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| Abstract: | Let MD,E,F= be an upper triangular operator matrix on the Hilbert space H1⊕H2⊕H3. In this paper, we obtain necessary and sufficient conditions of σ*(MD,E,F)=σ*(A) ∪ σ*(B) ∪ σ*(C) for every D ∈ B(H2, H1), E ∈ B(H3, H1) and F ∈ B(H3, H2), in terms of the spectral properties of diagonal entries A, B and C in MD,E,F, where σ* is the point spectrum, the residual spectrum and the continuous spectrum. Moreover, we construct some examples illustrating our main results. |
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| Keywords: | point spectrum residual spectrum continuous spectrum 3× 3 upper triangular operator matrix |
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