Weyl's Theorem, a‐Weyl's Theorem, and Local Spectral Theory
Weyl's Theorem, a‐Weyl's Theorem, and Local Spectral Theory
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DOI：
10.1112/s0024610702004027
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发表时间：
2002-07
期刊：
影响因子：
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通讯作者：
R. Curto;Y. Han
中科院分区：
文献类型：
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作者：
R. Curto;Y. Han
给出了具有单值可拓性质的Banach空间算子满足Weyl定理和a - Weyl定理的充分必要条件。证明了如果T或T*具有单值可拓性且T是泛面，则对于f∈H(σ(T)), f(T)的Weyl定理成立。当T*具有单值可扩性时，T是泛面且T是等值面，则对于f∈H(σ(T)), f(T)的a - Weyl定理成立。还证明了如果T或T*具有单值可拓性，则谱映射定理对Weyl谱和本质近似点谱成立。
Necessary and sufficient conditions are given for a Banach space operator with the single‐valued extension property to satisfy Weyl's theorem and a‐Weyl's theorem. It is shown that if T or T* has the single‐valued extension property and T is transaloid, then Weyl's theorem holds for f(T)for every f∈H(σ(T)). When T* has the single‐valued extension property, T is transaloid and T is a‐isoloid, then a‐Weyl's theorem holds for f(T) for every f∈H(σ(T)). It is also proved that if T or T* has the single‐valued extension property, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.