{"paper":{"title":"Some extensions of the Young and Heinz inequalities for Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","submitted_at":"2017-05-07T09:29:50Z","abstract_excerpt":"In this paper, we present some extensions of the Young and Heinz inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with matrices. More precisely, for two positive semidefinite matrices $A$ and $B$ we show that\n  \\begin{align*} \\Big\\|A^{\\nu}XB^{1-\\nu}+A^{1-\\nu}XB^{\\nu}\\Big\\|_{2}^{2}\\leq\\Big\\|AX+XB\\Big\\|_{2}^{2}- 2r\\Big\\|AX-XB\\Big\\|_{2}^{2}-r_{0}\\left(\\Big\\|A^{\\frac{1}{2}}XB^{\\frac{1}{2}}-AX\\Big\\|_{2}^{2}+ \\Big\\|A^{\\frac{1}{2}}XB^{\\frac{1}{2}}-XB\\Big\\|_{2}^{2}\\right), \\end{align*} where $X$ is an arbitrary $n\\times n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02585","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"}