{"paper":{"title":"Embedding Banach spaces into the space of bounded functions with countable support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Tomasz Kania, William B. Johnson","submitted_at":"2018-07-13T18:04:14Z","abstract_excerpt":"We prove that a WLD subspace of the space $\\ell_\\infty^c(\\Gamma)$ consisting of all bounded, countably supported functions on a set $\\Gamma$ embeds isomorphically into $\\ell_\\infty$ if and only if it does not contain isometric copies of $c_0(\\omega_1)$. Moreover, a subspace of $\\ell_\\infty^c(\\omega_1)$ is constructed that has an unconditional basis, does not embed into $\\ell_\\infty$, and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of $c_0(\\omega_1)$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05239","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"}