{"paper":{"title":"$\\ell_\\infty$-sums and the Banach space $\\ell_\\infty/c_0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"Christina Brech, Piotr Koszmider","submitted_at":"2012-11-14T01:04:46Z","abstract_excerpt":"This paper is concerned with the isomorphic structure of the Banach space $\\ell_\\infty/c_0$ and how it depends on combinatorial tools whose existence is consistent but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that $\\ell_\\infty/c_0$ does not have an orthogonal \\break $\\ell_\\infty$-decomposition that is, it is not of the form $\\ell_\\infty(X)$ for any Banach space $X$. The main local result is that it is consistent that $\\ell_\\infty(c_0(\\mathfrak{c}))$ does not embed isomorphically into $\\ell_\\infty/c_0$, where $\\mathfrak{c}$ is the cardinality of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3173","kind":"arxiv","version":2},"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"}