{"paper":{"title":"Sharpening Some Classical Numerical Radius Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H.R. Moradi, K. Shebrawi, M.E. Omidvar","submitted_at":"2017-08-08T01:30:43Z","abstract_excerpt":"New upper and lower bounds for the numerical radii of Hilbert space operators are given. Among our results, we prove that if $A\\in \\mathcal{B} \\left( \\mathcal{H}\\right) $ is a hyponormal operator, then for all non-negative non-decreasing operator convex $f$ on $ [0,\\infty ),$ we have \\[f\\left( \\omega \\left( A \\right) \\right)\\le \\frac{1}{2}\\left\\| f\\left( \\frac{1}{1+\\frac{\\xi_{\\left| A \\right|}^{2}}{8}}\\left| A \\right| \\right)+f\\left( \\frac{1}{1+\\frac{\\xi_{\\left| A \\right|}^{2}}{8}}\\left| {{A}^{*}} \\right| \\right) \\right\\|,\\] where ${{\\xi }_{\\left| A\\right| }}=\\underset{\\left| x\\right| =1}{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02345","kind":"arxiv","version":2},"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"}