称T ∈ B(H)有广义Kato分解,若存在一对T的闭的不变子空间(M, N), 使得H=M⊕N,其中T|M为上半Fredholm算子且具有非负的指标, T|N是幂零的.本文利用算子的广义Kato分解性质,研究了Weyl型定理在紧摄动下的稳定性. 此外,还研究了2 × 2上三角算子矩阵的Weyl型定理在紧摄动下的稳定性.
Abstract
An operator T ∈ B(H) is said to admit a generalized Kato decomposition, if there exists a pair of T-invariant closed subspaces (M,N) such that H=M⊕N, the restriction T|M is upper semi-Fredholm with ind(T|M) ≤ 0 and T|N is nilpotent. In this paper, using the property of generalized Kato decomposition of T ∈ B(H), we investigate the stability of the Weyl type theorem under compact perturbations. Also, we characterize 2×2 upper triangular operator matrices for which the Weyl type theorem is stable under compact perturbations.
关键词
Weyl型定理 /
紧摄动 /
广义Kato分解 /
上三角算子矩阵
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Key words
Weyl type theorem /
compact perturbations /
generalized Kato decomposition /
the upper triangular operator matrices
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参考文献
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脚注
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基金
陕西师范大学中央高校基本科研业务费专项资金资助项目(GK201301007)
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