{"paper":{"title":"Norm and anti-norm inequalities for positive semi-definite matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Fumio Hiai, Jean-Christophe Bourin","submitted_at":"2010-12-23T10:34:59Z","abstract_excerpt":"Some subadditivity results involving symmetric (unitarily invariant) norms are obtained. For instance, if $g(t)=\\sum_{k=0}^m a_kt^k$ is a polynomial of degree $m$ with non-negative coefficients, then, for all positive operators $A,\\,B$ and all symmetric norms, $\\|g(A+B)\\|^{1/m} \\le \\|g(A)\\|^{1/m} + \\|g(B)\\|^{1/m}$. To give parallel superadditivity results, we investigate anti-norms, a class of functionals containing the Schatten $q$-norms for $q\\in(0,1]$ and $q<0$. The results are extensions of the Minkowski determinantal inequality. A few estimates for block-matrices are derived. For instance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5171","kind":"arxiv","version":2},"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"}