{"paper":{"title":"Finite Rank Isopairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Udeni Wijesooriya","submitted_at":"2016-10-09T00:32:25Z","abstract_excerpt":"An algebraic isopair is a commuting pair of pure isometries that is annihilated by a polynomial defining a distinguished variety $\\mathcal{V}$. The notion of the rank of a pure algebraic isopair with finite bimultiplicity is introduced. For $\\mathcal{V} $, a union of $s$ irreducible varieties $\\mathcal{V}_j$, the rank is a $s$-tuple $\\alpha=(\\alpha_1,...,\\alpha_s)$ of natural numbers. A pure algebraic isopair of finite bimultiplicity with rank $\\alpha$ is described as a restriction of a $\\max\\{\\alpha_1,...,\\alpha_s\\}$-cyclic pure algebraic isopair to a finite codimensional invariant subspace. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02602","kind":"arxiv","version":2},"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"}