{"paper":{"title":"Primariness of the spaces $\\ell_p(C(K))$ for $1 \\leq p \\leq \\infty$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Acuaviva","submitted_at":"2026-05-28T12:36:00Z","abstract_excerpt":"We prove that the spaces $\\ell_p(C(\\alpha))$ and $\\ell_p(C[0,1])$ have the uniform primary factorisation property whenever $\\alpha$ is an ordinal and $1<p\\leq\\infty$. For the case $p=1$, we establish a general criterion ensuring that $\\ell_1(X)$ inherits the uniform primary factorisation property from $X$. As a consequence, $\\ell_p(C(K))$ is primary for every compact metrizable space $K$ and every $1 \\leq p \\leq \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29854","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/2605.29854/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"}