{"paper":{"title":"Closed ideals with bounded $\\Delta$-weak approximate identities in some certain Banach algebras","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javad Laali, Mohammad Fozouni","submitted_at":"2014-10-20T06:05:53Z","abstract_excerpt":"It is shown that a locally compact group $G$ is amenable if and only if some certain closed ideals of the Fig\\`{a}-Talamanca-Herz algebra $A_{p}(G)$ admit bounded $\\Delta$-weak approximate identities. Also, similar results are obtained for the function algebras $\\mathfrak{L}A(G)$ and $C_{0}^{w}(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5159","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":""},"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"}