王济荣,曹小红.性质$(\omega)$的注解[J].数学研究及应用,2011,31(1):100~108 |
性质$(\omega)$的注解 |
A Note on Property $(\omega)$ |
投稿时间:2009-08-10 修订日期:2010-04-27 |
DOI:10.3770/j.issn:1000-341X.2011.01.011 |
中文关键词: 逼近Weyl定理 性质$(\omega)$ Browder算子. |
英文关键词:approximate Weyl's theorem property $(\omega)$ Browder operator. |
基金项目:陕西师范大学中央高校基本科研业务费专项基金(Grant No.GK200901015),教育部新世纪优秀人才支持计划资助项目(Grant No.2006),山西省重点学科扶持基金资助项目. |
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中文摘要: |
在本文中, 根据新定义的谱集,我们研究了由Rako$\mathrm{\breve{c}}$evi$\mathrm{\grave{c}}$介绍的Weyl定理的一种变化性质:性质$(\omega)$. 给出了Banach空间上有界线性算子同时满足性质$(\omega)$和逼近Weyl定理的充要条件. 利用所得的结论, 我们研究了$\lambda-$弱$-H(p)$算子的性质$(\omega)$和逼近Weyl定理. |
英文摘要: |
In this note we study the property $(\omega)$, a variant of Weyl's theorem introduced by Rako\v{c}evi\`{c}, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property $(\omega)$ and approximate Weyl's theorem hold. As a consequence of the main result, we study the property $(\omega)$ and approximate Weyl's theorem for a class of operators which we call the $\lambda$-weak-$H(p)$ operators. |
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