{"paper":{"title":"Refinements of a reversed AM-GM operator inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad","submitted_at":"2015-06-21T21:01:27Z","abstract_excerpt":"We prove some refinements of a reverse AM-GM operator inequality due to M. Lin [Studia Math. 2013;215:187-194]. In particular, we show the operator inequality\n  \\begin{eqnarray*} \\Phi^p\\left(A\\nabla_\\nu B+2rMm(A^{-1}\\nabla B^{-1}-A^{-1}\\sharp B^{-1})\\right)\\leq\\alpha^p\\Phi^p\\left(A\\sharp_\\nu B\\right), \\end{eqnarray*} where $A,B$ are positive operators on a Hilbert space such that $0<m \\leq A, B \\leq M$ for some positive numbers $m, M$, $\\Phi$ is a positive unital linear map, $\\nu\\in[0,1]$, $r=\\min\\{\\nu,1-\\nu\\}$, $p>0$ and $\\alpha=\\max\\left\\{\\frac{(M+m)^2}{4Mm},\\frac{(M+m)^2}{4^\\frac{2}{p}Mm}\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06414","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"}