{"paper":{"title":"Contractivity, Complete Contractivity and Curvature inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal","submitted_at":"2014-08-11T12:49:14Z","abstract_excerpt":"Let $\\|\\cdot\\|_{\\mathbf A}$ be a norm on $\\mathbb C^m$ given by the formula $\\|(z_1,\\ldots,z_m)\\|_{\\mathbf A}=\\|z_1A_1+\\cdots+z_mA_m\\|_{\\rm op}$ for some choice of an $m$-tuple of $n\\times n$ linearly independent matrices $\\mathbf A=(A_1, \\ldots, A_m).$ Let $\\Omega_\\mathbf A\\subset \\mathbb C^m$ be the unit ball with respect to the norm $\\|\\cdot\\|_{\\mathbf A}.$ %For a holomorphic function $f$ on $\\Omega_\\mathbf A,$ let %$\\rho_{V}(f):=\\left ( %\\begin{smallmatrix} %f(w)I_p& \\sum_{i=1}^{m} \\partial_if(w)V_{i} \\\\ %0 & f(w)I_q %\\end{smallmatrix}\\right ),$ where $V_1, \\ldots, V_m$ are $p\\times q$ %ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2389","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"}