{"paper":{"title":"Convex Multivariable Trace Functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Elliott H. Lieb, Gert K. Pedersen","submitted_at":"2001-07-08T18:28:01Z","abstract_excerpt":"For any densely defined, lower semi-continuous trace \\tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2, ..., x_n) --> \\tau (f(x_1, x_2, ..., x_n)) is convex on the space \\bigoplus_{i=1}^n (A_i)_{self-adjoint}. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called \\ell-convexity, show how it applies to traces, and give a few examples. In part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107062","kind":"arxiv","version":3},"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"}