{"paper":{"title":"(Non-)amenability of B(E)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"math.FA","authors_text":"Volker Runde","submitted_at":"2009-09-14T19:18:54Z","abstract_excerpt":"In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra $B(E)$ of all bounded linear operators on a Banach space $E$ could ever be amenable if $\\dim E = \\infty$. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros--Haydon result that solves the \"scalar plus compact problem\": there is an infinite-dimensional Banach space $E$, the dual of which is $\\ell^1$, such that $B(E) = K(E)+ \\mathbb{C} \\id_E$. Still, $B(\\ell^2)$ is not amenable, and in the past decade, $ B(\\ell^p)$ wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2628","kind":"arxiv","version":4},"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"}