{"paper":{"title":"On $\\Delta$-weak $\\phi$-amenability of Banach algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javad Laali, Mohammad Fozouni","submitted_at":"2014-03-10T08:37:13Z","abstract_excerpt":"Let $A$ be a Banach algebra and $\\phi\\in \\Delta(A)\\cup\\{0\\}$. We say that $A$ is $\\Delta$-weak $\\phi$-amenable if there exists an $m\\in A^{**}$ such that $m(\\phi)=0$ and $m(\\psi.a)=\\psi(a)$ for each $\\psi\\in \\Delta(A)$ and $a\\in \\ker(\\phi)$. It is shown that $A$ is $\\Delta$-weak $\\phi$-amenable if and only if $\\ker(\\phi)$ has a bounded $\\Delta$-weak approximate identity. We examine this notion for some algebras over amenable locally compact groups. Also we prove that every $\\Delta$-weak $\\phi$-amenable Banach algebra has a bounded $\\Delta$-weak approximate identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2162","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"}