The Equivalence between Property (ω) and Weyl’s Theorem

The Equivalence between Property (ω) and Weyl’s Theorem

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摘要 We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ B（H）, TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl＇s theorem and property （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered. We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ B（H）, TB and BT are Fredholm together and the same index of B, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl＇s theorem and property （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered.

作者 Ling Ling ZHAO Xiao Hong CAO He Jia ZHANG

机构地区 College of Mathematics and Information Science

出处《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期705-712,共8页 数学研究与评论（英文版）

基金 Supported by Plan of the New Century Talented Person of the Ministry of Education of China (Grant No.NCET-06-0870) the Fundamental Research Funds for the Central Universities (Grant GK200901015)

关键词 Weyl＇s theorem property （ω） SPECTRUM Weyl＇s theorem property （ω） spectrum

分类号 O177.2 [理学—基础数学]

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Journal of Mathematical Research and Exposition

2011年第4期

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The Equivalence between Property (ω) and Weyl’s Theorem

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