JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 34-40.doi: 10.6040/j.issn.1671-9352.0.2020.428

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Judgement of Browders theorem for bounded linear operators

SUN Chen-hui1, BAI Zhen-gui2, CAO Xiao-hong2   

  1. 1. School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China;
    2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2021-01-21

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Abstract: By using the newly defined spectrum set, Browders theorem which is a variant of Weyls theorem is studied. The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding Browders theorem are established. As a consequence of the main result, a new judgement of Browders theorem for operator function is discussed.

Key words: Browders theorem, spectrum, operator function

CLC Number: 

  • O177.1
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