{"paper":{"title":"Uniqueness of the maximal ideal of operators on the $\\ell_p$-sum of $\\ell_\\infty^n\\ (n\\in\\mathbb{N})$ for $1<p<\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2014-05-22T11:27:39Z","abstract_excerpt":"A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_p}$ and $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_1^n\\bigr)_{\\ell_p}$ whenever $p\\in(1,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5715","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"}