{"paper":{"title":"Advanced refinements of Young and Heinz inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Sababheh, Mohammad Sal Moslehian","submitted_at":"2016-06-22T08:25:47Z","abstract_excerpt":"In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \\begin{eqnarray*} A\\#_{\\nu}B&+&\\sum_{j=1}^{N}s_{j}(\\nu)\\left(A\\#_{\\alpha_j(\\nu)}B+A\\#_{2^{1-j}+\\alpha_j(\\nu)}B-2A\\#_{2^{-j}+\\alpha_j(\\nu)}B\\right)\\leq A\\nabla_{\\nu}B, \\end{eqnarray*} for the positive operators $A$ and $B$, where $0\\leq \\nu\\leq 1, N\\in\\mathbb{N}$ and $\\alpha_j(\\nu)$ is a certain function. Moreover, some new Heinz type inequalities involving the Hilbert-Schmidt norm are established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06848","kind":"arxiv","version":2},"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"}