{"paper":{"title":"On the monotonicity of weighted power means of matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jose Franco, Raluca Dumitru","submitted_at":"2017-01-24T13:57:10Z","abstract_excerpt":"Let $\\mu_p(A,B,t)=(tA^p+(1-t)B^p)^{1/p}$ denote the weighted power mean between positive operators $A$ and $B$. We show that the function $t\\to \\|A-\\mu_p(A,B,t)\\|_2$ is monotonically decreasing whenever $1/2 \\leq p \\leq 1$. Hence showing that the weighted power means satisfy Audenaert's \"in-betweenness\" property for positive operators for power satisfying $1/2 \\leq p \\leq 1$. We also show that when $p>2$ there exist operators for which the weighted power mean does not satisfy this \"in-betweenness\" property with respect to the Euclidean metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07023","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"}