{"paper":{"title":"Extensions of interpolation between the arithmetic-geometric mean inequality for matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Mojtaba Bakherad, Monire Hajmohamadi, Rahmatollah Lashkaripour","submitted_at":"2017-08-19T15:23:28Z","abstract_excerpt":"In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\\times n$ matrices, then \\begin{align*} \\|AXB^*\\|^2\\leq\\|f_1(A^*A)Xg_1(B^*B)\\|\\,\\|f_2(A^*A)Xg_2(B^*B)\\|, \\end{align*} where $f_1,f_2,g_1,g_2$ are non-negative continues functions such that $f_1(t)f_2(t)=t$ and $g_1(t)g_2(t)=t\\,\\,(t\\geq0)$. We also obtain the inequality \\begin{align*} \\left|\\left|\\left|AB^*\\right|\\right|\\right|^2\\nonumber&\\leq \\left|\\left|\\left|p(A^*A)^{\\frac{m}{p}}+ (1-p)(B^*B)^{\\frac{s}{1-p}}\\right|\\right|\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05862","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"}