CFI算子与(ω)性质和(ω1)性质的判定
CFI operators and the judgements of property (ω) and property (ω1)
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摘要: 利用一致Fredholm指标性质定义了一个新的谱集,根据这个谱集给岀了算子T及其共轭算子T*满足
\left( \omega _1 \right) 性质和\left( \omega \right) 性质的判定条件.并且,对Hilbert空间上有界线性算子的\left( \omega \right) 性质的与T交换的有限秩摄动F进行了讨论.Abstract: Using the new spectrum set defined by the property of consistency in Fredholm and index, we give the judgements of property\left( \omega _1 \right) and property\left( \omega \right) for a operator T and its adjoint operator T*. We also consider the stability of property\left( \omega \right) for a bounded linear operator acting on Hilbert space, under finite rank perturbations F commuting with T.