{"paper":{"title":"Zero Lie product determined Banach algebras, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. R. Villena, J. Alaminos, J. Extremera, M. Bresar","submitted_at":"2017-09-27T10:17:25Z","abstract_excerpt":"A Banach algebra $A$ is said to be zero Lie product determined if every continuous bilinear functional $\\varphi \\colon A\\times A\\to \\mathbb{C}$ satisfying $\\varphi(a,b)=0$ whenever $ab=ba$ is of the form $\\varphi(a,b)=\\omega(ab-ba)$ for some $\\omega\\in A^*$. We prove that $A$ has this property provided that any of the following three conditions holds: (i) $A$ is a weakly amenable Banach algebra with property $\\mathbb{B}$ and having a bounded approximate identity, (ii) every continuous cyclic Jordan derivation from $A$ into $A^*$ is an inner derivation, (iii) $A$ is the algebra of all $n\\times "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09432","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":""},"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"}