{"paper":{"title":"Squaring operator P\\'{o}lya--Szeg\\\"{o} and Diaz--Metcalf type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mohammad Sal Moslehian, Xiaohui Fu","submitted_at":"2015-01-13T10:08:22Z","abstract_excerpt":"We square operator P\\'{o}lya--Szeg\\\"{o} and Diaz--Metcalf type inequalities as follows: If operator inequalities $0<m_{1}^{2} \\leq A\\leq M_{1}^{2}$ and $0<m_{2}^{2}\\leq B\\leq M_{2}^{2}$ hold for some positive real numbers $m_{1}\\leq M_{1}$ and $m_{2}\\leq M_{2}$, then for every unital positive linear map $\\Phi$ the following inequalities hold: \\begin{eqnarray*}\n  (\\Phi(A)\\sharp\\Phi(B))^2 &\\leq&\\left(\\frac{M_1M_2 + m_1m_2}{2\\sqrt{M_1M_2m_1m_2}}\\right)^4\\Phi(A\\sharp B)^{2}\n  \\end{eqnarray*} and \\begin{eqnarray*} \\left( \\frac{M_2m_2}{M_1m_1}\\Phi (A) + \\Phi (B) \\right)^2 \\leq \\left( \\frac{(M_1m_1(M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02939","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"}