{"paper":{"title":"$\\Gamma$-unitaries, dilation and a natural example","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau, Tirthankar Bhattacharyya","submitted_at":"2013-11-07T05:06:26Z","abstract_excerpt":"This note constructs an explicit normal boundary dilation for a commuting pair $(S,P)$ of bounded operators with the symmetrized bidisk $$\\Gamma=\\{(z_1+z_2,z_1z_2):|z_1|,|z_2| \\leq 1\\}$$ as a spectral set. Such explicit dilations had hitherto been constructed only in the unit disk \\cite{sfr}, the unit bidisk \\cite{ando} and in the tetrablock \\cite{sir and me1}. The dilation is minimal and unique under a suitable condition. This paper also contains a natural example of a $\\Gamma$-isometry. We compute its associated fundamental operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1577","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"}