The essential numerical range for unbounded linear operators
The essential numerical range for unbounded linear operators
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DOI：
10.1016/j.jfa.2020.108509
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发表时间：
2020-07-15
影响因子：
1.7
通讯作者：
Tretter, Christiane
中科院分区：
文献类型：
--
作者：
Boegli, Sabine;Marletta, Marco;Tretter, Christiane
对无界Hilbert空间算子T引入本质数值域W-e（T）的概念，研究了它的基本性质，包括可能的等价刻画和扰动结果.许多已知的属性有界的情况下不结转到无界的情况下，和新的有趣的现象出现，我们说明了一些引人注目的例子。基本数值范围W-e（T）的一个关键特征是，当通过投影方法或偏微分方程的域截断方法近似T时，它以统一和最小的方式捕获光谱污染。(C)2020爱思唯尔公司All rights reserved.
We introduce the concept of essential numerical range W-e(T) for unbounded Hilbert space operators T and study its fundamental properties including possible equivalent characterizations and perturbation results. Many of the properties known for the bounded case do not carry over to the unbounded case, and new interesting phenomena arise which we illustrate by some striking examples. A key feature of the essential numerical range W-e(T) is that it captures spectral pollution in a unified and minimal way when approximating T by projection methods or domain truncation methods for PDEs. (C) 2020 Elsevier Inc. All rights reserved.