| 3×3上三角算子矩阵的Weyl型定理 |
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| 引用本文： | 曹小红.3×3上三角算子矩阵的Weyl型定理[J].数学学报,2006,49(3):529-538. |
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| 作者姓名： | 曹小红 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 西安 |
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| 基金项目： | 陕西师范大学校级青年基金资助项目 |
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| 摘 要： | 设A∈B(H1),B∈B(H2),C∈B(H3)为给定的三个算子,用M(D,E,F)= 表示一个作用在H1(?)H2(?)H3上的3×3算子矩阵．本文首先给出存在算子D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2),使得M(D,E,F)为上半Fredholm算子(下半Fredholm算子)的充要条件．同时研究了3×3算子矩阵 M(D,E,F)的Weyl定理,α-Weyl定理,Browder定理和α-Browder定理．
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| 关 键 词： | Browder定理 Weyl定理 谱 |
| 收稿时间： | 2004-11-8 |
Weyl's Theorem for 3×3 Upper Triangular Operator Matrices |
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| Xiao Hong CAO College of Mathematics and Information Science,Shaanxi Normal University,Xi'an ,P. R. China.Weyl's Theorem for 3×3 Upper Triangular Operator Matrices[J].Acta Mathematica Sinica,2006,49(3):529-538. |
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| Authors: | Xiao Hong CAO College of Mathematics and Information Science Shaanxi Normal University Xi'an P R China |
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| Institution: | Xiao Hong CAO College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
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| Abstract: | When A∈B(H1), B∈B(H2) and C∈B(H3) are given, we denote by M(D,E,F) an operator, acting on the Hilbert space H1H2H3, of the form M(D, E, F)= . In this paper, we give the necessary and sufficient condition for M(D,E,F) to be upper semi-Fredholm (lower semi-Fredholm) operator for some D∈B(H2,H1), E∈B(H3,H1), F∈B(H3,H2). Weyl type theorems are liable to fail for 2×2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, α-Weyl's theorem and α-Browder's theorem survive for 3×3 upper triangular operator matrices on the Hilbert space. |
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| Keywords: | Browder's theorem Weyl's theorem spectrum |
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