{"paper":{"title":"Thickness of the unit sphere, $\\ell_1$-types, and the almost Daugavet property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dirk Werner, Varvara Shepelska, Vladimir Kadets","submitted_at":"2009-02-26T14:47:54Z","abstract_excerpt":"We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\\eps$-net consisting of elements of $S_X$ for any $\\eps < 2$. We give characterisations of this class of spaces in terms of $\\ell_1$-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space $X$ is isomorphic to a space from this class if and only if $X$ contains an isomorphic copy of $\\ell_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4503","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"}