一致可逆性质及广义(ω)性质的摄动

曹小红, 辛巧玲

数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 91-100.

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数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 91-100. DOI: 10.12386/A2012sxxb0008
论文

一致可逆性质及广义(ω)性质的摄动

    曹小红, 辛巧玲
作者信息 +

Consistent Invertibility and Perturbations of the Generalized Property(ω)

    Xiao Hong CAO, Qiao Ling XIN
Author information +
文章历史 +

摘要

Hilbert空间算子TB(H)称为是一致可逆的,若对任意的SB(H), TSST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.  

Abstract

A Hilbert space operator TB(H)may be said to be “consistent in invertibility” provided that for each SB(H), TS and ST are either both or neither invertible. The induced spectrum contributes the stability of generalized property(ω), for a bounded operator T acting on a Hilbert space, under perturbations by finite rank operators, by nilpotent operators and quisi-nilpotent operators commuting with T. The stability of generalized property(ω)of the operators which are the products of finitely normal operators are considered.  

关键词

广义(ω)性质 / 摄动 / 一致可逆性质

Key words

generalized property(ω) / perturbation / consistent in invertibility

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导出引用
曹小红, 辛巧玲. 一致可逆性质及广义(ω)性质的摄动. 数学学报, 2012, 55(1): 91-100 https://doi.org/10.12386/A2012sxxb0008
Xiao Hong CAO, Qiao Ling XIN. Consistent Invertibility and Perturbations of the Generalized Property(ω). Acta Mathematica Sinica, Chinese Series, 2012, 55(1): 91-100 https://doi.org/10.12386/A2012sxxb0008

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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(GK200901015)

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