赵玲玲, 高凯, 洪明理, 王福昌. 算子函数的a-Weyl定理和($\mathcal{R} $)性质[J]. 华南师范大学学报（自然科学版）, 2023, 55(5): 80-87. doi: 10.6054/j.jscnun.2023066
引用本文: 赵玲玲, 高凯, 洪明理, 王福昌. 算子函数的a-Weyl定理和($\mathcal{R} $)性质[J]. 华南师范大学学报（自然科学版）, 2023, 55(5): 80-87. doi: 10.6054/j.jscnun.2023066
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ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property($\mathcal{R} $) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. doi: 10.6054/j.jscnun.2023066
Citation: ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property($\mathcal{R} $) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. doi: 10.6054/j.jscnun.2023066
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算子函数的a-Weyl定理和(\mathcalR )性质

a-Weyl's Theorem and Property(\mathcalR ) for Operator Functions

    摘要
  • 摘要: 文章利用谱集的关系给出判定有界线性算子分别满足a-Weyl定理和(\mathcalR )性质的新方法, 在此基础上, 得到算子同时满足a-Weyl定理和(\mathcalR )性质的充要条件；然后，讨论了算子函数满足a-Weyl定理和(\mathcalR )性质的充要条件, 最终得到算子函数同时满足a-Weyl定理和(\mathcalR )性质的判定方法。

     

    Abstract: The new judgements for which a-Weyl's theorem, property (\mathcalR ), both a-Weyl's theorem and property (\mathcalR ) hold are given. In additional, the necessary and sufficient conditions for operator functions to satisfy the a-Weyl's theorem, the property (\mathcalR ), both the a-Weyl's theorem and the property (\mathcalR ) are considered.

     

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