{"paper":{"title":"A generalization of POWERS-ST{\\O}RMER inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Anchal Aggarwal, Mandeep Singh","submitted_at":"2016-06-13T12:10:20Z","abstract_excerpt":"Let $A,\\;B$ be the positive semidefinite matrices. A matrix version of the famous Powers-St{\\o}rmer's inequality $$2Tr(A^\\alpha B^{1-\\alpha})\\geq Tr(A+B-|A-B|),\\;\\;\\;0\\leq\\alpha\\leq 1,$$ was proven by Audenaert et. al. We establish a comparison of eigenvalues for the matrices $A^\\alpha B^{1-\\alpha}$ and $A+B-|A-B|, \\; 0 \\leq \\alpha \\leq 1,$ subsuming the Powers-St{\\o}rmer's inequality. We also prove several related norm inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03913","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"}