{"paper":{"title":"Continuity properties of best analytic approximation","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nicholas J. Young, Vladimir V. Peller","submitted_at":"1995-11-28T00:00:00Z","abstract_excerpt":"Let $\\A$ be the operator which assigns to each $m \\times n$ matrix-valued function on the unit circle with entries in $H^\\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \\times n$ matrix-valued functions in the open unit disc. We study the continuity of $\\A$ with respect to various norms. Our main result is that, for a class of norms satifying certain natural axioms, $\\A$ is continuous at any function whose superoptimal singular values are non-zero and is such that certain associated integer indices are equal to 1. We also obtain necessary conditions for cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9511214","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"}