{"paper":{"title":"Very badly approximable matrix functions","license":"","headline":"","cross_cats":["math.CA","math.CO","math.CT","math.CV"],"primary_cat":"math.FA","authors_text":"S.R. Treil, V.V. Peller","submitted_at":"2003-03-15T17:45:55Z","abstract_excerpt":"We study in this paper very badly approximable matrix functions on the unit circle $\\T$, i.e., matrix functions $\\Phi$ such that the zero function is a superoptimal approximation of $\\Phi$. The purpose of this paper is to obtain a characterization of the continuous very badly approximable functions.\n Our characterization is more geometric than algebraic characterizations earlier obtained in \\cite{PY} and \\cite{AP}. It involves analyticity of certain families of subspaces defined in terms of Schmidt vectors of the matrices $\\Phi(\\z)$, $\\z\\in\\T$. This characterization can be extended to the wide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303186","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"}