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The essential numerical range for unbounded linear operators.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
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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