{"paper":{"title":"Contractivity and complete contractivity for finite dimensional Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal, Cherian Varughese, Gadadhar Misra","submitted_at":"2016-04-07T04:23:09Z","abstract_excerpt":"Choose an arbitrary but fixed set of $n\\times n$ matrices $A_1, \\ldots, A_m$ and let $\\Omega_\\mathbf A\\subset \\mathbb C^m$ be the unit ball with respect to the norm $\\|\\cdot\\|_{\\mathbf A},$ where $\\|(z_1,\\ldots ,z_m)\\|_{\\mathbf A}=\\|z_1A_1+ \\cdots+z_mA_m\\|_{\\rm op}.$ It is known that if $m\\geq 3$ and $\\mathbb B$ is any ball in $\\mathbb C^m$ with respect to some norm, say $\\|\\cdot\\|_{\\mathbb B},$ then there exists a contractive linear map $L:(\\mathbb C^m,\\|\\cdot\\|^*_{\\mathbb B})\\to \\mathcal M_k$ which is not completely contractive. The characterization of those balls in $\\mathbb C^2$ for which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01872","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"}