{"paper":{"title":"Grothendieck's theorem for absolutely summing multilinear operators is optimal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Pellegrino, Juan B. Seoane-Sepulveda","submitted_at":"2013-07-18T00:57:58Z","abstract_excerpt":"Grothendieck's theorem asserts that every continuous linear operator from $\\ell_{1}$ to $\\ell_{2}$ is absolutely $\\left( 1;1\\right) $-summing. In this note we prove that the optimal constant $g_{m}$ so that every continuous $m$-linear operator from $\\ell_{1}\\times\\cdots\\times\\ell_{1}$ to $\\ell_{2}$ is absolutely $\\left( g_{m};1\\right) $-summing is $\\frac{2}{m+1}$. We also show that if $g_{m}<\\frac{2}{m+1}$ there is $\\mathfrak{c}$ dimensional linear space composed by continuous non absolutely $\\left( g_{m};1\\right) $-summing $m$-linear operators from $\\ell_{1}\\times\\cdots\\times\\ell_{1}$ to $\\el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4809","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"}