{"paper":{"title":"Closed ideals of operators on and complemented subspaces of Banach spaces of functions with countable support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gideon Schechtman, Tomasz Kania, William B. Johnson","submitted_at":"2015-02-10T18:17:14Z","abstract_excerpt":"Let $\\lambda$ be an infinite cardinal number and let $\\ell_\\infty^c(\\lambda)$ denote the subspace of $\\ell_\\infty(\\lambda)$ consisting of all functions that assume at most countably many non-zero values. We classify all infinite dimensional complemented subspaces of $\\ell_\\infty^c(\\lambda)$, proving that they are isomorphic to $\\ell_\\infty^c(\\kappa)$ for some cardinal number $\\kappa$. Then we show that the Banach algebra of all bounded linear operators on $\\ell_\\infty^c(\\lambda)$ or $\\ell_\\infty(\\lambda)$ has the unique maximal ideal consisting of operators through which the identity operator "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03026","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"}