{"paper":{"title":"Ando dilations, von Neumann inequality, and distinguished varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"B. Krishna Das, Jaydeb Sarkar","submitted_at":"2015-10-15T18:23:13Z","abstract_excerpt":"Let $\\mathbb{D}$ denote the unit disc in the complex plane $\\mathbb{C}$ and let $\\mathbb{D}^2 = \\mathbb{D} \\times \\mathbb{D}$ be the unit bidisc in $\\mathbb{C}^2$. Let $(T_1, T_2)$ be a pair of commuting contractions on a Hilbert space $\\mathcal{H}$. Let $\\mbox{dim } \\mbox{ran}(I_{\\mathcal{H}} - T_j T_j^*) < \\infty$, $j = 1, 2$, and let $T_1$ be a pure contraction. Then there exists a variety $V \\subseteq \\overline{\\mathbb{D}}^2$ such that for any polynomial $p \\in \\mathbb{C}[z_1, z_2]$, the inequality \\[ \\|p(T_1,T_2)\\|_{\\mathcal{B}(\\mathcal{H})} \\leq \\|p\\|_V \\] holds. If, in addition, $T_2$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04655","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"}