The Judgment of Weyl's Theorem and Property (R)
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摘要: 利用半Fredholm算子的扰动不变性，研究有界线性算子与上三角算子矩阵的Weyl型定理。首先，给出有界线性算子同时满足Browder定理和(R1)性质，或者同时满足Weyl定理和(R)性质的充要条件；然后，讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。Abstract: The perturbation invariance of semi-Fredholm operators are used to study Weyl type theorems for boun-ded linear operators and upper triangular operator matrices. First, the necessary and sufficient conditions for which both the property(R1) and Browder's theorem hold or both the property (R) and Weyl's theorem hold for bounded linear operators are given. In addition, the conditions for which both the property (R) and Weyl's theorem hold for upper triangular operator matrices are explored.
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