The essential numerical range for unbounded linear operators

Bögli, Sabine; Marletta, Marco; Tretter, Christiane

Abstract

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.

Citation

Bögli, S., Marletta, M., & Tretter, C. (2020). The essential numerical range for unbounded linear operators. Journal of Functional Analysis, 279(1), Article 108509. https://doi.org/10.1016/j.jfa.2020.108509

• 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
• DOI: https://doi.org/10.1016/j.jfa.2020.108509