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The essential numerical range for unbounded linear operators

Bögli, Sabine; Marletta, Marco; Tretter, Christiane

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Sabine Bögli

Marco Marletta

Christiane Tretter



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.


Bögli, S., Marletta, M., & Tretter, C. (2020). The essential numerical range for unbounded linear operators. Journal of Functional Analysis, 279(1), Article 108509.

Journal Article Type Article
Acceptance Date Jan 24, 2020
Online Publication Date Feb 8, 2020
Publication Date Jul 15, 2020
Deposit Date Feb 10, 2020
Publicly Available Date Feb 8, 2021
Journal Journal of Functional Analysis
Print ISSN 0022-1236
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 279
Issue 1
Article Number 108509


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