Bögli, Sabine and Marletta, Marco and Tretter, Christiane (2020) 'The essential numerical range for unbounded linear operators.', Journal of functional analysis., 279 (1). p. 108509.
We introduce the concept of essential numerical range 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 is that it captures spectral pollution in a unified and minimal way when approximating T by projection methods or domain truncation methods for PDEs.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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|Publisher Web site:||https://doi.org/10.1016/j.jfa.2020.108509|
|Publisher statement:||© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/|
|Date accepted:||24 January 2020|
|Date deposited:||11 February 2020|
|Date of first online publication:||08 February 2020|
|Date first made open access:||08 February 2021|
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