{"paper":{"title":"Operators which are polynomially isometric to a normal operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Laurent W. Marcoux, Yuanhang Zhang","submitted_at":"2019-08-19T19:07:25Z","abstract_excerpt":"Let $\\mathcal{H}$ be a complex, separable Hilbert space and $\\mathcal{B}(\\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\\mathcal{H}$. Given a unitarily-invariant norm $\\| \\cdot \\|_u$ on $\\mathcal{B}(\\mathcal{H})$ and two linear operators $A$ and $B$ in $\\mathcal{B}(\\mathcal{H})$, we shall say that $A$ and $B$ are \\emph{polynomially isometric relative to} $\\| \\cdot \\|_u$ if $\\| p(A) \\|_u = \\| p(B) \\|_u$ for all polynomials $p$. In this paper, we examine to what extent an operator $A$ being polynomially isometric to a normal operator $N$ implies that $A$ is itself no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07029","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07029/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"}