{"paper":{"title":"Epigraph of Operator Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohsen Kian","submitted_at":"2015-12-17T11:04:26Z","abstract_excerpt":"It is known that a real function $f$ is convex if and only if the set $$\\mathrm{E}(f)=\\{(x,y)\\in\\mathbb{R}\\times\\mathbb{R};\\ f(x)\\leq y\\},$$ the epigraph of $f$ is a convex set in $\\mathbb{R}^2$. We state an extension of this result for operator convex functions and $C^*$-convex sets as well as operator log-convex functions and $C^*$-log-convex sets. Moreover, the $C^*$-convex hull of a Hermitian matrix has been represented in terms of its eigenvalues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05529","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"}