{"paper":{"title":"A weak*-topological dichotomy with applications in operator theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Piotr Koszmider, Tomasz Kania","submitted_at":"2013-02-28T21:26:05Z","abstract_excerpt":"Denote by $[0,\\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\\omega_1]$.\n  Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\\omega_1)$ can either be embedded in a Hilbert-ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0020","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"}