{"paper":{"title":"A General Double Inequality Related to Operator Means and Positive Linear Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"J. S. Aujla, M. Singh, M. S. Moslehian, R. Kaur","submitted_at":"2012-04-23T12:59:27Z","abstract_excerpt":"Let $A,B\\in \\mathbb{B}(\\mathscr{H})$ be such that $0<b_{1}I \\leq A \\leq a_{1}I$ and $0<b_{2}I \\leq B \\leq a_{2}I$ for some scalars $0<b_{i}< a_{i},\\;\\; i=1,2$ and $\\Phi:\\mathbb{B}(\\mathscr{H})\\rightarrow\\mathbb{B}(\\mathscr{K})$ be a positive linear map. We show that for any operator mean $\\sigma$ with the representing function $f$, the double inequality $$ \\omega^{1-\\alpha}(\\Phi(A)#_{\\alpha}\\Phi(B))\\le (\\omega\\Phi(A))\\nabla_{\\alpha}\\Phi(B)\\leq \\frac{\\alpha}{\\mu}\\Phi(A\\sigma B) $$ holds, where $\\mu=\\frac{a_{1}b_{1}(f(b_{2}a_{1}^{-1})-f(a_{2}b_{1}^{-1}))}{b_{1}b_{2}-a_{1}a_{2}}, $ $\\nu=\\frac{a_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5049","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"}