Spectral inclusion and spectral pollution results are proved for sequences of linear operators of the form $T_0 + i \gamma s_n$ on a Hilbert space, where $s_n$ is strongly convergent to the identity operator and $\gamma > 0$. We work in both an abstract setting and a more concrete Sturm-Liouville framework. The results provide rigorous justification for a method of computing eigenvalues in spectral gaps.

中文翻译：

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一类耗散扰动的光谱包含和污染

证明了 Hilbert 空间上 $T_0 + i \gamma s_n$ 形式的线性算子序列的光谱包含和光谱污染结果，其中 $s_n$ 与恒等算子强收敛且 $\gamma > 0$。我们在抽象的环境和更具体的 Sturm-Liouville 框架中工作。结果为计算光谱间隙中的特征值的方法提供了严格的理由。