一般地,若T满足(ω)性质,即使K是有限秩算子或紧算子,T+K也不一定有(ω)性质.根据本质逼近点谱的变形与一致可逆算子定义的谱集,给出了(ω)性质及其摄动的充要条件,并将所得结论应用于代数拟A类算子.
In general, property (ω) holding for T is not transmitted to the perturbation T+K, even when K is a finite-rank operator or compact operator. We discussed the sufficient and necessary conditions for property (ω) and its stability by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency invertibility. Using these results, we studied the case of algebraically quasi-class A operators.
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