{"paper":{"title":"Analytic Model of Doubly Commuting Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OA"],"primary_cat":"math.FA","authors_text":"E. K. Narayanan, Jaydeb Sarkar, T. Bhattacharyya","submitted_at":"2013-10-03T12:09:12Z","abstract_excerpt":"An n-tuple (n \\geq 2), T = (T_1, \\ldots, T_n), of commuting bounded linear operators on a Hilbert space \\mathcal{H} is doubly commuting if T_i T_j^* = T_j^* T_i for all $1 \\leq i < j \\leq n$. If in addition, each T_i \\in C_{\\cdot 0}, then we say that T is a doubly commuting pure tuple. In this paper we prove that a doubly commuting pure tuple $T$ can be dilated to a tuple of shift operators on some suitable vector-valued Hardy space H^2_{\\mathcal{D}_{T^*}}(\\mathbb{D}^n). As a consequence of the dilation theorem, we prove that there exists a closed subspace \\mathcal{S}_T of the form \\[\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0950","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"}