{"paper":{"title":"On the Dilation Theory and Canonical Decomposition of $\\mathbf{\\Theta}_n$-Contractions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Aparna Gupta, Avijit Pal, Bhaskar Paul","submitted_at":"2026-08-04T12:32:26Z","abstract_excerpt":"This paper studies the domain $\\mathbf{\\Theta}_n$ from the perspective of operator theory. We obtain several characterizations of $\\mathbf{\\Theta}_n$-contractions (respectively, $\\mathbf{\\Theta}_n$-unitaries and $\\mathbf{\\Theta}_n$-isometries) and establish their relationships with $\\Gamma_n$-contractions (respectively, $\\Gamma_n$-unitaries and $\\Gamma_n$-isometries), tetrablock contractions (respectively, tetrablock unitaries and tetrablock isometries), and $\\mathbf{\\Theta}_{n+1}$-contractions (respectively, $\\mathbf{\\Theta}_{n+1}$-unitaries and $\\mathbf{\\Theta}_{n+1}$-isometries). We prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03574","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03574/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}