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Riesz Idempotent and Weyl’s Theorem for w-hyponormal Operators
被引：0
作者：
Young Min Han
Jun Ik Lee
Derming Wang
机构：
[1] Kyunghee University,Department of Mathematics
[2] California State University,Department of Mathematics
[3] Long Beach,undefined
来源：
Integral Equations and Operator Theory
|
2005年
/
53卷
关键词：
Primary 47A10;
47A53;
47B20;
-hyponormal operators;
Weyl’s theorem;
single valued extension property;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let T be a w-hyponormal operator on a Hilbert space H,
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\begin{document}$$\widetilde T$$\end{document} its Aluthge transform, λ an isolated point of the spectrum of T, and Eλ and
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\begin{document}$$ \widetilde E_{\lambda }$$\end{document} the Riesz idempotents, with respect to λ, of T and
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\begin{document}$$ \widetilde T, $$\end{document} respectively. It is shown that
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\begin{document}$$E_{\lambda } H = \widetilde E_{\lambda } H.$$\end{document} Consequently, Eλ is self-adjoint,
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\begin{document}$$E_{\lambda } = \widetilde E_{\lambda } $$\end{document} and
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\begin{document}$$ E_{\lambda } H = \ker (T - \lambda ) = \ker (T - \lambda )^*$$\end{document} if λ ≠ 0. Moreover, it is shown that Weyl’s theorem holds for f(T), where f ∈ H(σ (T)).
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页码：51 / 60
页数：9
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