{"paper":{"title":"Bilinear Ideals in Operator Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Maite Fern\\'andez-Unzueta, Ver\\'onica Dimant","submitted_at":"2013-06-14T14:30:13Z","abstract_excerpt":"We introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces. In particular, we study the bilinear ideals $\\mathcal{N}$ of completely nuclear, $\\mathcal{I }$ of completely integral, $\\mathcal{E}$ of completely extendible bilinear mappings, $\\mathcal{MB}$ multiplicatively bounded and its symmetrization $\\mathcal{SMB}$. We prove some basic properties of them, one of which is the fact that $\\mathcal{I}$ is naturally identified with the ideal of (linear) completely integral mappings on the injective operator space tensor product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3411","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"}