{"paper":{"title":"Upper and Lower Bounds for Numerical Radii of Block Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hwa-Long Gau, Pei Yuan Wu","submitted_at":"2014-10-01T19:22:00Z","abstract_excerpt":"For any $n$-by-$n$ matrix $A$ of the form \\[[\\begin{array}{cccc} 0 & A_1 & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & A_{k-1} \\\\ & & & 0\\end{array}],\\] we consider two $k$-by-$k$ matrices \\[A'=[\\begin{array}{cccc} 0 & \\|A_1\\| & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & \\|A_{k-1}\\| \\\\ & & & 0\\end{array}] \\ {and} \\ A''=[\\begin{array}{cccc} 0 & m(A_1) & & \\\\ & 0 & \\ddots & \\\\ & & \\ddots & m(A_{k-1}) \\\\ & & & 0\\end{array}],\\] where $\\|\\cdot\\|$ and $m(\\cdot)$ denote the operator norm and minimum modulus of a matrix, respectively. It is shown that the numerical radii $w(\\cdot)$ of $A$, $A'$ and $A''$ are related"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0339","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":""},"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"}