{"paper":{"title":"A reflexive Banach space whose algebra of operators is not a Grothendieck space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Tomasz Kania","submitted_at":"2012-11-13T01:34:18Z","abstract_excerpt":"By a result of Johnson, the Banach space $F=(\\bigoplus_{n=1}^\\infty \\ell_1^n)_{\\ell_\\infty}$ contains a complemented copy of $\\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive space $(\\bigoplus_{n=1}^\\infty \\ell_1^n)_{\\ell_p}$ ($p\\in (1,\\infty))$, thus giving a negative answer to the problem posed in the monograph of Diestel and Uhl which asks whether the space of operators on a reflexive Banach space is Grothendieck."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2867","kind":"arxiv","version":3},"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"}