{"paper":{"title":"Numerical radius of certain two-by-two block matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Hwa-Long Gau, Jia-Huo Hong, Kuo-Zhong Wang","submitted_at":"2026-06-07T11:12:40Z","abstract_excerpt":"We investigate the numerical range $W(T)$ and numerical radius $w(T)$ of operators of the form $T = \\begin{pmatrix} A & B \\\\ 0 & 0 \\end{pmatrix}$. We show that $W(T)$ is the union of the numerical ranges of a family of $2\\times 2$ matrices, $T_x$, leading to several consequences, including improved inequalities for $w(T)$. For cases where $A$ is a self-adjoint involution, we characterize the conditions under which $W(T)$ is an elliptical disk and determine the minimum numerical radius of $T_U = \\begin{pmatrix} U^*AU & B \\\\ 0 & 0 \\end{pmatrix}$ over all unitary operators $U$. Finally, we study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08576","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08576/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}