{"paper":{"title":"B(l^p) is never amenable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Volker Runde","submitted_at":"2009-07-23T16:16:04Z","abstract_excerpt":"We show that, if $E$ is a Banach space with a basis satisfying a certain condition, then the Banach algebra $\\ell^\\infty({\\cal K}(\\ell^2 \\oplus E))$ is not amenable; in particular, this is true for $E = \\ell^p$ with $p \\in (1,\\infty)$. As a consequence, $\\ell^\\infty({\\cal K}(E))$ is not amenable for any infinite-dimensional ${\\cal L}^p$-space. This, in turn, entails the non-amenability of ${\\cal B}(\\ell^p(E))$ for any ${\\cal L}^p$-space $E$, so that, in particular, ${\\cal B}(\\ell^p)$ and ${\\cal B}(L^p[0,1])$ are not amenable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.3984","kind":"arxiv","version":7},"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"}