On the ellipticity of the higher rank numerical range
Functional Analysis
2026-03-23 v2
Abstract
The higher rank numerical range is a concept that generalizes the classical numerical range, and it has application in quantum error correction. We investigate these sets for -by- block matrices with associated Kippenhahn curves consisting of ellipses (and eventually points). As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky {\it et al}.
Keywords
Cite
@article{arxiv.2512.02977,
title = {On the ellipticity of the higher rank numerical range},
author = {Natália Bebiano and Rute Lemos and Graça Soares},
journal= {arXiv preprint arXiv:2512.02977},
year = {2026}
}
Comments
16 pages, 1 figure; revised text, corollary and remark moved from Section 2 to Section 3, previous Theorem 3.7 replaced by new Remark 3.2, restatement and condensed proofs for the last theorem and corollary