{"paper":{"title":"The symmetric Radon-Nikod\\'ym property for tensor norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Carando, Daniel Galicer","submitted_at":"2010-05-15T15:30:26Z","abstract_excerpt":"We introduce the symmetric-Radon-Nikod\\'ym property (sRN property) for finitely generated s-tensor norms $\\beta$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $\\beta$ is a projective s-tensor norm with the sRN property, then for every Asplund space $E$, the canonical map $\\widetilde{\\otimes}_{\\beta}^{n,s} E' \\to \\Big(\\widetilde{\\otimes}_{\\beta'}^{n,s} E \\Big)'$ is a metric surjection. This can be rephrased as the isometric isomorphism $\\mathcal{Q}^{min}(E) = \\mathcal{Q}(E)$ for certain polynomial ideal $\\Q$. We also relate the sRN prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2683","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"}