三阶上三角关系矩阵的本质谱性质
Essential Spectral Properties of Third-Order Upper Triangular Relation Matrices
DOI: 10.12677/pm.2025.155167, PDF,   
作者: 赵 娜：内蒙古师范大学数学科学学院，内蒙古 呼和浩特
关键词: 关系矩阵；本质谱；Weyl谱；本质近似点谱；Relation Matrix； Essential Spectrum； Weyl Spectrum； Essential Approximation Point Spectrum
摘要: 设 H 1 , H 2 , H 3 为无穷维复可分Hilbert空间，对给定关系 A∈ℬℛ( H 1 ),B∈ℬℛ( H 2 ),C∈ℬℛ( H 3 ) ，记 M D,E,F =( A D E 0 B F 0 0 C )∈ℬℛ( H 1 ⊕ H 2 ⊕ H 3 ) ，本文讨论了 D∈ℬℛ( H 2 , H 1 ) ， E∈ℬℛ( H 3 , H 1 ) ， F∈ℬℛ( H 3 , H 2 ) 时 M D,E,F 的本质谱、Weyl谱和本质近似点谱包含关系成立的条件。
Abstract: Let H 1 , H 2 , H 3 be infinite-dimensional complex separable Hilbert spaces, given the relation A∈ℬℛ( H 1 ),B∈ℬℛ( H 2 ),C∈ℬℛ( H 3 ) , and write M D,E,F =( A D E 0 B F 0 0 C )∈ℬℛ( H 1 ⊕ H 2 ⊕ H 3 ) . In this paper, a necessary and sufficient condition is given for the essential spectrum, Weyl spectrum, essential approximation point spectrum for M D,E,F with D∈ℬℛ( H 2 , H 1 ) , E∈ℬℛ( H 3 , H 1 ) , F∈ℬℛ( H 3 , H 2 ) .
文章引用：赵娜. 三阶上三角关系矩阵的本质谱性质[J]. 理论数学, 2025, 15(5): 185-193. https://doi.org/10.12677/pm.2025.155167

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