Property (w) and perturbations
Property (w) and perturbations
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DOI：
10.1016/j.jmaa.2007.02.084
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发表时间：
2007-12
影响因子：
1.3
通讯作者：
P. Aiena
中科院分区：
文献类型：
--
作者：
P. Aiena
定义在Banach空间X上的有界线性算子T∈L（X）满足性质（w），即Weyl定理的一个变体，如果Weyl本质近似谱σwa（T）的近似点谱σa（T）中的补集与谱的所有孤立点的集合重合，这些孤立点是有限重特征值。本文研究了Banach空间上有界算子T在有限秩算子、幂零算子和拟幂零算子扰动下性质（w）的稳定性。
A bounded linear operator T∈L(X) defined on a Banach space X satisfies property (w), a variant of Weyl's theorem, if the complement in the approximate point spectrum σa(T) of the Weyl essential approximate spectrum σwa(T) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T.