| 孙晨辉,曹小红.算子矩阵的(R1)性质与(R)性质[J].数学年刊A辑,2025,46(1):65~74 |
| 算子矩阵的(R1)性质与(R)性质 |
| Property (R1) and Property (R) for Operator Matrices |
| Received:January 19, 2024 Revised:February 04, 2025 |
| DOI：10.16205/j.cnki.cama.2025.0003 |
| 中文关键词: （R1)性质 (R)性质 谱 算子矩阵 |
| 英文关键词:Property (R1) Property (R) Spectrum Operator matrices |
| 基金项目:2022年度渭南市科技局科技计划项目(No.2022ZDYFJH-11),
2024年渭南师范学院服务渭南市基础教育高质量发展教育科学研究专项课题(No.SWNZ2420)和
渭南师范学院2021年人才项目(No.2021RC16) |
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| 中文摘要: |
| (R)性质是Weyl型定理的最新变形,
突出反映了线性算子的特征值与升标的关系. 作者
通过运用主对角线上给定算子谱子集的特点研究算子矩阵,
给出了2×2上三角算子矩阵满足(R1)性质与(R)性质的充要条件. |
| 英文摘要: |
| Property (R) which is the latest variations of Weyl type theorem reflects the
relation between eigenvalues and ascents of linear operators prominently. By using the
characteristics of the spectral subset of the given operators on the main diagonal to study the
operator matrix, the necessary and sufficient conditions for 2 × 2 upper triangular operator
matrices holding property (R1) and property (R) are established. |
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