{"paper":{"title":"Explicit and unique construction of tetrablock unitary dilation in a certain case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau, Tirthankar Bhattacharyya","submitted_at":"2014-12-14T14:23:34Z","abstract_excerpt":"Consider the domain $E$ in $\\mathbb{C}^3$ defined by\n  $$\n  E=\\{(a_{11},a_{22},\\text{det}A): A=\\begin{pmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{pmatrix}\\text{ with }\\lVert A \\rVert <1\\}.\n  $$\n  This is called the tetrablock. This paper constructs explicit boundary normal dilation for a triple $(A,B,P)$ of commuting bounded operators which has $\\bar{E}$ as a spectral set.\n  We show that the dilation is minimal and unique under a certain natural condition. As is well-known, uniqueness of minimal dilation usually does not hold good in several variables, e.g., Ando's dilation is not known t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4363","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":""},"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"}