Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H), TS与ST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 T ∈ B(H)may be said to be “consistent in invertibility” provided that for each S ∈ B(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
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Key words
generalized property(ω) /
perturbation /
consistent in invertibility
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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(GK200901015)
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