{"paper":{"title":"Generality of Lieb's Concavity Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"De Huang","submitted_at":"2019-05-30T21:37:01Z","abstract_excerpt":"We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function $\\phi:\\mathbf{H}^n_+\\rightarrow \\mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) \\mapsto\\phi\\big[(B^\\frac{qs}{2}K^*A^{ps}KB^\\frac{qs}{2})^{\\frac{1}{s}}\\big] $ on $\\mathbf{H}_+^m\\times\\mathbf{H}_+^n$, for any $K\\in \\mathbb{C}^{m\\times n},s\\in(0,1],p,q\\in[0,1], p+q\\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00002","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"}