{"paper":{"title":"Some inequalities of matrix power and Karcher means for positive linear maps","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":"2017-02-24T08:06:01Z","abstract_excerpt":"In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite matrices such that $0<m\\leq A_{i}\\leq M\\, (i=1,\\cdots,n)$ for some scalars $m< M$ and $\\omega=(w_{1},\\cdots,w_{n})$ is a weight vector with $w_{i}\\geq0$ and $\\sum_{i=1}^{n}w_{i}=1$, then \\begin{align*} \\Phi^{p}\\Big(\\sum_{i=1}^{n}w_{i}A_{i}\\Big)\\leq \\alpha^{p}\\Phi^{p}(P_{t}(\\omega; {\\mathbb A})) \\end{align*} and \\begin{align*} \\Phi^{p}\\Big(\\sum_{i=1}^{n}w_{i}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07488","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"}