3×3阶上三角算子矩阵的点谱、剩余谱和连续谱
The Point, Residual and Continuous Spectrum of 3×3 Upper Triangular Operator Matrices
记MD,E,F=为Hilbert空间H1⊕H2⊕H3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*(MD,E,F)=σ*(A)∪σ*(B)∪σ*(C)对任意D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2)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.
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.
点谱 / 剩余谱 / 连续谱 / 3× / 3阶上三角算子矩阵 {{custom_keyword}} /
point spectrum / residual spectrum / continuous spectrum / 3× / 3 upper triangular operator matrix {{custom_keyword}} /
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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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