{"paper":{"title":"Improvements of some operator inequalities involving positive linear maps via the Kantorovich constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Leila Nasiri, Mojtaba Bakherad","submitted_at":"2018-01-06T15:11:08Z","abstract_excerpt":"We present some operator inequalities for positive linear maps that generalize and improve the derived results in some recent years. For instant, if $A$ and $B$ are positive operators and $m,m^{'},M,M^{'}$ are positive real numbers satisfying either one of the condition $ 0<m \\leq B \\leq m^{'} <M^{'} \\leq A \\leq M $ or $0<m \\leq A \\leq m^{'} <M^{'} \\leq B \\leq M$, then \\begin{align*} \\Phi ^{p} \\big(A \\nabla _{v} B+2 r Mm (A^{-1}\\nabla B^{-1}- &A^{-1} \\sharp B^{-1} )\\big)\\\\ & \\leq \\left( \\frac{K(h)}{ 4^{\\frac{2}{p}-1} K^{r_{1}} \\left( \\sqrt {h^{'}}\\right)} \\right) ^{p} \\Phi^{p} (A \\sharp_{\\nu} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02030","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"}