| 一类本质正规算子的稳定不变子空间 |
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| 引用本文： | 翟发辉. 一类本质正规算子的稳定不变子空间[J]. 应用泛函分析学报, 2001, 3(3): 197-201 |
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| 作者姓名： | 翟发辉 |
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| 作者单位： | 青岛化工学院数学所山东青岛 266042 |
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| 基金项目： | The work was supported in partby The Heilongjiang Science Foundation( 1 96 71 0 1 8) |
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| 摘 要： | 在本文中 ,我们给出了一类本质正规算子的稳定不变子空间的特征 .即 ,T∈ L( H2 ( Ω;μ) )且满足1 ) T是本质正规算子 ;2 )σ( T) =Ω,σe( T) = Ω,σp( T) =Ω ;3) ind( T-z) =n,z∈Ω;4 ) minind( T-z) =0 ,z∈ Ω.M是 T的非平凡的不变子空间 ,则 M是 T的稳定不变子空间当且仅当 dim M<∞ and dim M⊥ =∞
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| 关 键 词： | 稳定不变子空间 本质正规算子 广义右预解射影 边界线性算子 Hilbert空间 |
The Stable Invariant Subspace of Certain Essentially Normal Operators |
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| ZHAI Fa-hui. The Stable Invariant Subspace of Certain Essentially Normal Operators[J]. Acta Analysis Functionalis Applicata, 2001, 3(3): 197-201 |
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| Authors: | ZHAI Fa-hui |
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| Affiliation: | ZHAI Fa-hui Institute of Mathematics,Qingdao Institute of Chemical Technology,Qingdao Shandong 266042,China |
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| Abstract: | In this paper, we give the character of stable invariant subspace of certain essentially normal operators, i.e, T∈L(H2(Ω;μ)) and T satisfies the following conditions ① T is an essentially normal; ②σ(T)=Ω,σc(T)=Ω,σp(T)=Ω; ③ind(T z)=n, z∈Ω; ④minind(T z)=0, z∈Ω. IfMisanontrivial invariant subspace of T, then M is a stable invariant subspace of T if and only if dimM＜∞ and dimM⊥ = ∞. |
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| Keywords: | stable invariant subspace essentially normal operator generalized right resolve projection |
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