{"paper":{"title":"New inequalities for operator concave functions involving positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H.R. Moradi, M.E. Omidvar, S. Sheybani","submitted_at":"2017-11-14T05:48:10Z","abstract_excerpt":"The purpose of this paper is to present some general inequalities for operator concave functions which include some known inequalities as a particular case. Among other things, we prove that if $A\\in \\mathcal{B}\\left( \\mathcal{H} \\right)$ is a positive operator such that $mI\\le A\\le MI$ for some scalars $0<m<M$ and $\\Phi $ is a normalized positive linear map on $\\mathcal{B}\\left( \\mathcal{H} \\right)$, then \\[\\begin{aligned} {{\\left( \\frac{M+m}{2\\sqrt{Mm}} \\right)}^{r}}&\\ge {{\\left( \\frac{\\frac{1}{\\sqrt{Mm}}\\Phi \\left( A \\right)+\\sqrt{Mm}\\Phi \\left( {{A}^{-1}} \\right)}{2} \\right)}^{r}} & \\ge \\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04957","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"}