| 无穷维Hamilton算子纯虚谱的扰动 |
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| 引用本文： | 黄俊杰,阿拉坦仓. 无穷维Hamilton算子纯虚谱的扰动[J]. 内蒙古大学学报(自然科学版), 2008, 39(1): 1-6 |
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| 作者姓名： | 黄俊杰 阿拉坦仓 |
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| 作者单位： | 内蒙古大学数学系,呼和浩特,010021;内蒙古大学数学系,呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金 , 内蒙古自然科学基金 , 内蒙古大学校科研和教改项目 |
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| 摘 要： | 研究了Hilbert空间X⊕X中的无穷维Hamilton算子HC=[A C 0 -A*]和HF=[A F B -A*]的纯虚谱的扰动,其中R(B)是闭的.给定算子A,B,证明了∩C∈S(X)σi(HC)=σiπ(A),∪C∈S(X)σi(HC)=σi(A),∩F∈S(X)σi(HF)=σiπ(APR(B)⊥),∪F∈S(X)σi(HF)=σi(APR(B)⊥),其中σi(T),σiπ(T),PM和S(X)分别表示T的纯虚谱,纯虚近似谱,全空间到M的正交投影和X中的所有自伴算子所成之集.
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| 关 键 词： | 无穷维Hamilton算子 纯虚谱 扰动 |
| 文章编号： | 1000-1638（2008）01-0001-06 |
| 收稿时间： | 2007-04-24 |
| 修稿时间： | 2007-04-24 |
Perturbations of Pure Imaginary Spectra of Infinite Dimensional Hamiltonian Operators |
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| HUANG Jun-jie,Alatancang. Perturbations of Pure Imaginary Spectra of Infinite Dimensional Hamiltonian Operators[J]. Acta Scientiarum Naturalium Universitatis Neimongol, 2008, 39(1): 1-6 |
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| Authors: | HUANG Jun-jie Alatancang |
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| Abstract: | For infinite dimensional Hamiltonian operators HC=[A C 0 -A*] and HF=[A F B -A*] with closed R(B) in the Hilbert space X⊕X, the perturbations of pure imaginary spectra are studied.If A,B are given, one sees that ∩C∈S(X)σi(HC)=σiπ(A),∪C∈S(X)σi(HC)=σi(A),∩F∈S(X)σi(HF)=σiπ(APR(B)⊥),∪F∈S(X)σi(HF)=σi(APR(B)⊥),where σi(T),σiπ(T),PM and S(X) denote the pure imaginary spectrum of T,the pure imaginary approximate point spectrum of T,the orthogonal projection (from X) onto M and the set of all self-adjoint operators (not necessarily bounded) in X,respectively. |
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| Keywords: | infinite dimensional Hamiltonian operator pure imaginary spectrum perturbation |
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