{"paper":{"title":"Dilations of \\Gamma-contractions by solving operator equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sourav Pal, Subrata Shyam Roy, Tirthankar Bhattacharyya","submitted_at":"2011-08-03T07:52:43Z","abstract_excerpt":"For a contraction P and a bounded commutant S of P, we seek a solution X of the operator equation S-S*P = (I-P*P)^1/2 X(I-P*P) 1/2, where X is a bounded operator on Ran(I-P*P) 1/2 with numerical radius of X being not greater than 1. A pair of bounded operators (S,P) which has the domain \\Gamme = {(z 1 +z 2, z 1z 2) : |z1|{\\leq} 1, |z2| {\\leq}1} {\\subseteq} C2 as a spectral set, is called a \\Gamme-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a \\Gamma-contraction (S,P). This allows us to construct an explicit \\Gamma-isometric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0774","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"}