{"paper":{"title":"A note on some inequalities for positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"H.R. Moradi, I.H. G\\\"um\\\"u\\c{s}, M.E. Omidvar, R. Naseri","submitted_at":"2017-01-12T17:31:27Z","abstract_excerpt":"We improve and generalize some operator inequalities for positive linear maps. It is shown, among other inequalities, that if $0<m\\le B\\le m'<M'\\le A\\le M$ or $0<m\\le A\\le m'<M'\\le B\\le M$, then for each $2\\le p<\\infty $ and $\\nu \\in \\left[ 0,1 \\right]$, \\begin{equation*} {{\\Phi }^{p}}\\left( A{{\\nabla }_{\\nu }}B \\right)\\le {{\\left( \\frac{K\\left( h \\right)}{{{4}^{\\frac{2}{p}-1}}{{K}^{r}}\\left( h' \\right)} \\right)}^{p}}{{\\Phi }^{p}}\\left( A{{\\#}_{\\nu }}B \\right), \\end{equation*} and \\begin{equation*} {{\\Phi }^{p}}\\left( A{{\\nabla }_{\\nu }}B \\right)\\le {{\\left( \\frac{K\\left( h \\right)}{{{4}^{\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03428","kind":"arxiv","version":3},"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"}