{"paper":{"title":"Optimal estimates for summing multilinear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Gustavo Araujo","submitted_at":"2014-03-24T18:00:03Z","abstract_excerpt":"We show that given a positive integer $m$, a real number $p\\in\\left[ 2,\\infty\\right)$ and $1\\leq s<p^{\\ast}$ the set of non--multiple $\\left( r;s\\right)$--summing $m$--linear forms on $\\ell_{p}\\times\\cdots\\times \\ell_{p}$ contains, except for the null vector, a closed subspace of maximal dimension whenever $r<\\frac{2ms}{s+2m-ms}$. This result is optimal since for $r\\geq\\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\\ell_{p}\\times \\cdots\\times\\ell_{p}$ are multiple $\\left( r;s\\right)$--summing. In particular, among other results, we generalize a result related to cotype (from 2010) due to Botel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6064","kind":"arxiv","version":4},"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"}