{"paper":{"title":"Fekete's lemma in Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Aleksei Kulikov, Feng Shao","submitted_at":"2024-11-26T12:39:55Z","abstract_excerpt":"For a sequence of vectors $\\{v_n\\}_{n\\in\\mathbb{N}}$ in the uniformly convex Banach space $X$ which for all $n, m\\in \\mathbb{N}$ satisfy $\\|v_{n+m}\\|\\le \\|v_n + v_m\\|$ we show the existence of the limit $\\lim_{n\\to \\infty} \\frac{v_n}{n}$. This extends the classical Fekete's subadditivite lemma to Banach space-valued sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17380/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"}