{"paper":{"title":"And\\^o dilations for a pair of commuting contractions: two explicit constructions and functional models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau","submitted_at":"2017-10-31T08:20:52Z","abstract_excerpt":"One of the most important results in operator theory is And\\^o's \\cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit constructions (Sch\\\"affer \\cite{sfr} and Douglas \\cite{Doug-Dilation}) of the minimal isometric dilation of a single contraction, there was no such explicit construction of an And\\^o dilation for a commuting pair $(T_1,T_2)$ of contractions, except in some special cases \\cite{A-M-Dist-Var, D-S, D-S-S}. In this paper, we give two new proofs of And\\^o's dilation theorem b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11368","kind":"arxiv","version":4},"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"}