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The essential numerical range for unbounded linear operators

Bogli, Sabine, Marletta, Marco and Tretter, Christiane 2020. The essential numerical range for unbounded linear operators. Journal of Functional Analysis 279 (1) , 108509. 10.1016/j.jfa.2020.108509

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We introduce the concept of essential numerical range We(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 We(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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Elsevier
ISSN: 0022-1236
Date of First Compliant Deposit: 7 February 2020
Date of Acceptance: 24 January 2020
Last Modified: 09 Feb 2021 22:39

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