| 非正常算子局部谱的若干结果 |
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| 引用本文： | 严从荃.非正常算子局部谱的若干结果[J].赣南师范学院学报,1987(Z1). |
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| 作者姓名： | 严从荃 |
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| 作者单位： | 赣南师范学院数学系 |
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| 摘 要： | 在本文,我们得到下列结果 1.设T是完全非正常的协亚正常算子,且具单位延拓性质,假设D=TT~*-T~*T满足:是闭的。若△是闭园盘且△°∩σ(T)≠φ,则存在非零元x∈H使得σT(X)(?)△。 2.设T是θ一类算子,则T有单位延拓性质,若T满足σ(T)∩R′=φ,则谱子空间X_T(δ)是闭的,这里δ是C的闭子集,且T有非平凡的不变子空间。
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Some Results of the Local Spectra of the Non-normal Operators |
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| Abstract: | In thisPaPer, webtain the following results. 1. Let T be a completely non -normal cohyponormal operator with the single valued extension property and suppose D = T-T*-T*Tsatisfies: d∈Ru(D)бT(d) is closed. If Δ is a closed disc with Δ°∩б(T)φ, then there is a non-zero vector x∈H such that бT ( x ) Δ.2. Let T be aθ-class operator, then T has the single valued extension property. If T satisfies also б(T)∩|R'=<φ>,? then the spectral subspace XT (δ) is closed for any closed subset δofC, and T has a nontrivial invariant subspace. |
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