Bögli, Sabine; Marletta, Marco; Tretter, Christiane (2020). The essential numerical range for unbounded linear operators. Journal of functional analysis, 279(1), p. 108509. Elsevier 10.1016/j.jfa.2020.108509
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We introduce the concept of essential numerical range W_e(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 W_e(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: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Tretter, Christiane |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0022-1236 |
Publisher: |
Elsevier |
Funders: |
[4] Swiss National Science Foundation ; [UNSPECIFIED] Early Postdoc Mobility project ; [UNSPECIFIED] Imperial College London Chapman Fellowship |
Language: |
English |
Submitter: |
Sebastiano Don |
Date Deposited: |
10 Feb 2021 15:03 |
Last Modified: |
05 Dec 2022 15:45 |
Publisher DOI: |
10.1016/j.jfa.2020.108509 |
ArXiv ID: |
1907.09599 |
Uncontrolled Keywords: |
Essential numerical range, Numerical range, Eigenvalue approximation, Spectral pollution |
BORIS DOI: |
10.48350/151246 |
URI: |
https://boris.unibe.ch/id/eprint/151246 |
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