Numerical ranges of antilinear operators

0586519 - MÚ 2025 RIV CH eng J - Journal Article
Kołaczek, D. - Müller, Vladimír
Numerical ranges of antilinear operators.
Integral Equations and Operator Theory. Roč. 96, č. 2 (2024), č. článku 17. ISSN 0378-620X. E-ISSN 1420-8989
Institutional support: RVO:67985840
Keywords : antilinear operators * Banach space * numerical index * numerical radius
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00020-024-02768-5

We study numerical ranges of antilinear operators on both Hilbert and Banach spaces. We prove that the numerical range of an antilinear operator on at least two-dimensional space is always a disc, and so a convex set. This improves existing results. We also study other properties known for numerical ranges of linear operators and discuss similarities and differences in the antilinear setting.
Permanent Link: https://hdl.handle.net/11104/0353989