| 算子的拟相似与(Q)类算子 |
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| 引用本文： | 林辰,严子锟.算子的拟相似与(Q)类算子[J].数学学报,1997,40(2):259-264. |
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| 作者姓名： | 林辰 严子锟 |
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| 作者单位： | 福建师范大学数学系 福州350007
(林辰)，福建师范大学数学系 福州350007(严子锟) |
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| 摘 要： | 本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.
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| 关 键 词： | Hilbert空间 有界线性算子 谱 本质谱 拟相似 |
| 收稿时间： | 1995-8-29 |
| 修稿时间： | 1996-4-4 |
Quasisimilarity of Operators and (Q) Operators |
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| Lin Chen Yan Zikun.Quasisimilarity of Operators and (Q) Operators[J].Acta Mathematica Sinica,1997,40(2):259-264. |
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| Authors: | Lin Chen Yan Zikun |
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| Institution: | Lin Chen Yan Zikun (Department of Mathematics, Fujian Normal University, Fuzhou 350007, China) |
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| Abstract: | In this paper, we introduce the conceptions S∈ (Q) S∈ L(H) with σe(S) C σe(T) for every operator T quasisimilar to S, β(S) = {λ∈C : a neighbourhood U of λ such that (S -z) ○(V,H) is closed for every neighbour hood V of λ, V U}, characterize (Q) operators by means of β(S) and show that the family of (Q) operators includes many familiar operators (such as subdecompasable, M-hyponormal, semi-hyponormal operators, etc.) and is norm-dense in L(H). |
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| Keywords: | Hilbert space Bounded linear operator Spectrum Essential spectrum Quasisimilarity |
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