{"paper":{"title":"On polynomial $n$-tuples of commuting isometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Edward J. Timko","submitted_at":"2016-04-21T15:53:09Z","abstract_excerpt":"We extend some of the results of Agler, Knese, and McCarthy [1] to $n$-tuples of commuting isometries for $n>2$. Let $\\mathbb{V}=(V_1,\\dots,V_n)$ be an $n$-tuple of a commuting isometries on a Hilbert space and let Ann$(\\mathbb{V})$ denote the set of all $n$-variable polynomials $p$ such that $p(\\mathbb{V})=0$. When Ann$(\\mathbb{V})$ defines an affine algebraic variety of dimension 1 and $\\mathbb{V}$ is completely non-unitary, we show that $\\mathbb{V}$ decomposes as a direct sum of $n$-tuples $\\mathbb{W}=(W_1,\\dots,W_n)$ with the property that, for each $i=1,\\dots,n$, $W_i$ is either a shift o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06364","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"}