广义Kato分解与Weyl型定理的摄动

戴磊, 曹小红, 肖娜娜

数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 469-478.

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数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 469-478. DOI: 10.12386/A2013sxxb0048
论文

广义Kato分解与Weyl型定理的摄动

    戴磊, 曹小红, 肖娜娜
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Generalized Kato Decomposition and Perturbations for the Weyl Type Theorem

    Lei DAI, Xiao Hong CAO, Na Na XIAO
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摘要

TB(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

Key words

Weyl type theorem / compact perturbations / generalized Kato decomposition / the upper triangular operator matrices

引用本文

导出引用
戴磊, 曹小红, 肖娜娜. 广义Kato分解与Weyl型定理的摄动. 数学学报, 2013, 56(4): 469-478 https://doi.org/10.12386/A2013sxxb0048
Lei DAI, Xiao Hong CAO, Na Na XIAO. Generalized Kato Decomposition and Perturbations for the Weyl Type Theorem. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 469-478 https://doi.org/10.12386/A2013sxxb0048

参考文献

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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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