{"paper":{"title":"The Bidual of a Radical Operator algebra can be Semisimple","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Charles John Read","submitted_at":"2014-03-24T14:09:49Z","abstract_excerpt":"The paper of S. Gulick [Sidney (Denny) L. Gulick, Commutativity and ideals in the biduals of topological algebras, Pacific J. Math 18 No. 1, 1966] contains some good mathematics, but it also contains an error. It claims that for a Banach algebra A, the intersection of the Jacobson radical of A** with A is precisely the radical of A (this is claimed for either of the Arens products on A** - in itself a reasonable claim, because A is always contained in the topological centre of A**, so a fixed a in A lies in the radical of A** with the first Arens product, if and only if it lies in the radical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5958","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"}