共查询到17条相似文献,搜索用时 453 毫秒
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本文通过定义新的谱集,给出了算子满足a-Browder定理和a-Weyl定理的充要条件,运用了文章中新定义的谱集,研究了解析hyponormal算子的a-Weyl定理. 相似文献
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运用新的谱集,给出了有界线性算子同时满足(UWE)性质与a-Weyl定理的充要条件.之后利用主要结论,得到了2×2上三角算子矩阵及其函数同时满足(UWE)性质与a-Weyl定理的新的判定方法. 相似文献
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称Hilbert空间算子T∈B(H)满足a-Browder定理,如果σ_a(T)\σ_(aw)(T)=π_(00)~a(T),其中σ_a(T)和σ_(aw)(T)分别表示逼近点谱和Weyl本性逼近点谱,π_(00)~a(T)={λ∈isoσ_a(T),0dim N(T-λI)∞}.如果σ_a(T)\σ_(aw)(T)=π_(00)~A(T),称T满足a-Weyl定理.如果对所有的紧算子K,T+K都满足a-Browder定理(a-Weyl定理),则称T关于a-Browder定理(a-Weyl定理)是稳定性的.该文研究了a-Browder定理和a-Weyl定理的稳定性,给出了算子满足a-Browder定理和a-Weyl定理紧扰动的等价刻画. 相似文献
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A∈B(H)称为是一个Drazin可逆的算子,若A有有限的升标和降标.用σ_D(A)={λ∈C:A-λI不是Drazin可逆的)表示Drazin谱集.本文证明了对于Hilbert空间上的一个2×2上三角算子矩阵M_C=■,从σ_D(A)∪σ_D(G)到σ_D(M_C)的道路需要从前面子集中移动σ_D(A)∩σ_D(B)中一定的开子集,即有等式:σ_D(A)∪σ_D(B)=σ_D(M_C)∪G,其中G为σ_D(M_C)中一定空洞的并,并且为σ_D(A)∪σ_D(B)的子集.2×2算子矩阵不一定满足Weyl定理,利用Drazin谱,我们研究了2×2上三角算子矩阵的Weyl定理,Browder定理,a-Weyl定理和a-Browder定理. 相似文献
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Weyl定理反映了算子特征值的分布特点.运用新的谱集,给出了有界线性算子满足Weyl定理的新的判定方法.进一步通过该谱集,刻画了算子函数满足Weyl定理的充要条件. 相似文献
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研究了有界线性算子的(h)性质和(gh)性质的问题.利用算子的单值扩张性的方法,获得了Banach空间上有界线性算子的(h)性质和(gh)性质的几个充分必要条件以及它们与其他Weyl型定理之间的关系,(h)性质和(gh)性质是a-Weyl定理和广义a-Weyl定理的推广. 相似文献
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本文研究了具有单值扩张性的上三角算子矩阵半Fredholm性,利用单值扩张性与分块算子升标、降标、零维、亏维之间的联系,得到了具有单值扩张性的上三角算子矩阵半Fredholm性刻画,给出了用对角算子刻画上三角算子矩阵半Fredholm性的条件,并研究了算子矩阵半Fredholm性的扰动问题;此外,利用所得结果研究了上三角算子矩阵的谱、本质谱和Browder谱,同时进一步考虑了Browder定理,a-Browder定理,Weyl定理,a-Weyl定理,从局部谱的角度揭示了定理之间的联系,得到了定理成立的新条件并举例验证. 相似文献
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Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2006,323(1):267-274
Using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for T for which the a-Browder's theorem or the a-Weyl's theorem holds. Also, the relation between hypercyclic operators (or supercyclic operators) and the operators which satisfy Weyl type theorem is discussed. 相似文献
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Xiaohong Cao 《Proceedings of the American Mathematical Society》2007,135(6):1701-1708
In this note, the relation between hypercyclic operator matrices (or supercyclic operator matrices) and the operator matrices which satisfy Weyl type theorems is discussed. Also, using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for for which a-Browder's theorem or a-Weyl's theorem holds.
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关于广义Aluthge变换的谱性质的研究 总被引:2,自引:0,他引:2
设T∈H(H),T=U|T|是算子T的极分解,则定义T^λ=|T|^λU|T|^1-λ和T^λ(*)=|T*|^λU|T*|^1-λ,(其中0〈λ〈1)分别为算子的广义Aluthge变换和广义*-Aluthge变换.本文中主要研究了三者之间的几种谱的关系.同时,还证明了算子T满足修正的Weyl定理当且仅当弘满足修正的Weyl定理当且仅当T^λ(*)满足修正的Weyl定理.最后证明了算子T满足a—Weyl定理当且仅当T^λ满足a—Weyl定理. 相似文献
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Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2006,320(2):795-803
Using the new spectrum set defined in this note, we give the necessary and sufficient condition for T which the Weyl's theorem holds. We also consider how the Weyl's theorem survives for analytically Class A operators. 相似文献
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Xiaohong Cao Maozheng Guo Bin Meng 《Proceedings of the American Mathematical Society》2005,133(10):2977-2984
The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder's theorem to hold.
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Weyl spectra and Weyl's theorem 总被引:1,自引:0,他引:1
Xiaohong Cao Maozheng Guo Bin Meng 《Journal of Mathematical Analysis and Applications》2003,288(2):758-767
Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coincides with the Browder spectrum then Weyl's theorem holds, and conversely for isoloid operators. 相似文献