The essential numerical range for unbounded linear operators

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

[img] Text
1-s2.0-S0022123620300525-main.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (909kB) | Request a copy
[img]
Preview
Text
1907.09599.pdf - Submitted Version
Available under License Publisher holds Copyright.

Download (870kB) | Preview

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:

18 Feb 2021 10:20

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

Actions (login required)

Edit item Edit item
Provide Feedback