3×3阶上三角算子矩阵的点谱、剩余谱和连续谱

吴秀峰, 黄俊杰

数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 817-832.

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数学学报 ›› 2019, Vol. 62 ›› Issue (6) : 817-832. DOI: 10.12386/A2019sxxb0075
论文

3×3阶上三角算子矩阵的点谱、剩余谱和连续谱

    吴秀峰, 黄俊杰
作者信息 +

The Point, Residual and Continuous Spectrum of 3×3 Upper Triangular Operator Matrices

    Xiu Feng WU, Jun Jie HUANG
Author information +
文章历史 +

摘要

MD,E,F=为Hilbert空间H1H2H3上的上三角算子矩阵.我们借助对角元A,BC的谱性质给出了σ*MD,E,F)=σ*A)∪σ*B)∪σ*C)对任意DBH2H1),EBH3H1),FBH3H2)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.

Abstract

Let MD,E,F= be an upper triangular operator matrix on the Hilbert space H1H2H3. In this paper, we obtain necessary and sufficient conditions of σ*(MD,E,F)=σ*(A) ∪ σ*(B) ∪ σ*(C) for every DB(H2, H1), EB(H3, H1) and FB(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.

关键词

点谱 / 剩余谱 / 连续谱 / / 3阶上三角算子矩阵

Key words

point spectrum / residual spectrum / continuous spectrum / / 3 upper triangular operator matrix

引用本文

导出引用
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. 数学学报, 2019, 62(6): 817-832 https://doi.org/10.12386/A2019sxxb0075
Xiu Feng WU, Jun Jie HUANG. The Point, Residual and Continuous Spectrum of 3×3 Upper Triangular Operator Matrices. Acta Mathematica Sinica, Chinese Series, 2019, 62(6): 817-832 https://doi.org/10.12386/A2019sxxb0075

参考文献

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基金

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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