{"paper":{"title":"On Hastings' approach to Lin's Theorem for Almost Commuting Matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"David Herrera","submitted_at":"2020-11-23T23:54:28Z","abstract_excerpt":"Lin's theorem states that for all $\\epsilon > 0$, there is a $\\delta > 0$ such that for all $n \\geq 1$ if self-adjoint contractions $A,B \\in M_n(\\mathbb{C})$ satisfy $\\|[A,B]\\|< \\delta$ then there are self-adjoint contractions $A',B' \\in M_n(\\mathbb{C})$ with $[A',B']=0$ and $\\|A-A'\\|,\\|B-B'\\|<\\epsilon$. We present fully explained and corrected details of the approach in arXiv:0808.2474, which was the first version of Lin's theorem to provide asymptotic estimates.\n  We also apply this method to the case where $B$ is a normal matrix with spectrum lying in some nice 1-dimensional subset of $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.11800","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/2011.11800/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"}