数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1500-1506.

• 论文 • 上一篇    下一篇

Weyl型定理的稳定性

田俊红1|曹小红2|戴磊3   

  1. 1.天水师范学院 数学与统计学院 甘肃 天水 |741001;
    2.陕西师范大学数学与信息科学学院 西安 |716000;
    3.渭南师范学院数学与信息科学学院 陕西 渭南 |714099
  • 收稿日期:2012-12-24 修回日期:2014-05-19 出版日期:2014-12-25 发布日期:2014-12-25
  • 基金资助:

    陕西省自然科学基金(2014JQ1015)、渭南市科技计划项目(2013KYJ-1)和天水师范学院中青年教师科研资助项目(TS201205)资助

The Stability of the Weyl Type Theorem

 TIAN Jun-Hong1, CAO Xiao-Hong2, DAI Lei3   

  1. 1.College of Mathematica and Sta., Tianshui Normal University, Tianshui, 741001;
    2.College of Mathematica and |Information Science, |Shaanxi Normal University, Xi'an 710060;
    3.College of Mathematica |and |Information |Science, Weinan Normal University, |Weinan |714099
  • Received:2012-12-24 Revised:2014-05-19 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    陕西省自然科学基金(2014JQ1015)、渭南市科技计划项目(2013KYJ-1)和天水师范学院中青年教师科研资助项目(TS201205)资助

摘要:

称Hilbert 空间算子TB(H) 满足a-Browder 定理, 如果σa(T)\σaw(T)πa00(T), 其中σa(T) 和σaw(T) 分别表示逼近点谱和 Weyl 本性逼近点谱,  πa00(T)={λiso σa(T), 0N(T-λI)<∞}. 如果σa(T)\σaw(T)=πa00(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.

关键词: a-Browder 定理, a-Weyl 定理, 紧扰动

Abstract:

A Hilbert space operator T is said to satisfy a-Browder's theorem if σa(T)\σawa00(T), where σa(T) and σaw(T) denote the approximate point spectrum and the Weyl essential approximate point spectrum respectively, and πa00(T)={λiso σa(T), 0N(T-λI)<∞}. If σa(T)\σaw(T)=πa00(T), we say T satisfies a-Weyl's theorem.TB(H) is said to have the stability of the a-Browder's (a-Weyl's) theorem if T+K satisfies the a-Browder's (a-Weyl's) theorem for all compact operators K. In this note, we investigate the stability of the a-Browder's theorem and the a-Weyl's theorem, and we characterize those operators for which the a-Browder's theorem and the a-Weyl's theorem are stable under compact perturbations.

Key words: a-Browder´s theorem, a-Weyl´s theorem, Compact perturbation

中图分类号: 

  • 47A55