{"paper":{"title":"Lushness, numerical index 1 and the Daugavet property in rearrangement invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dirk Werner, Javier Meri, Miguel Martin, Vladimir Kadets","submitted_at":"2011-03-07T14:38:53Z","abstract_excerpt":"We show that for spaces with 1-unconditional bases lushness, the alternative Daugavet property and numerical index~1 are equivalent. In the class of rearrangement invariant (r.i.)\\ sequence spaces the only examples of spaces with these properties are $c_0$, $\\ell_1$ and $\\ell_\\infty$. The only lush r.i.\\ separable function space on $[0,1]$ is $L_1[0,1]$; the same space is the only r.i.\\ separable function space on $[0,1]$ with the Daugavet property over the reals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1282","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"}