{"paper":{"title":"Some inequalities for interpolational operator means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hamid Reza Moradi, Mohammad Sababheh, Shigeru Furuichi","submitted_at":"2018-08-25T01:35:54Z","abstract_excerpt":"Using the properties of geometric mean, we shall show for any $0\\le \\alpha ,\\beta \\le 1$, \\[f\\left( A{{\\nabla }_{\\alpha }}B \\right)\\le f\\left( \\left( A{{\\nabla }_{\\alpha }}B \\right){{\\nabla }_{\\beta }}A \\right){{\\sharp}_{\\alpha }}f\\left( \\left( A{{\\nabla }_{\\alpha }}B \\right){{\\nabla }_{\\beta }}B \\right)\\le f\\left( A \\right){{\\sharp}_{\\alpha }}f\\left( B \\right)\\] whenever $f$ is a non-negative operator log-convex function, $A,B\\in \\mathcal{B}\\left( \\mathcal{H} \\right)$ are positive operators, and $0\\le \\alpha ,\\beta \\le 1$. As an application of this operator mean inequality, we present several"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08342","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"}