{"paper":{"title":"Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anna Kami\\'nska, Hyung-Joon Tag","submitted_at":"2016-06-02T21:47:41Z","abstract_excerpt":"Given an Orlicz $N$-function $\\varphi$ and a positive decreasing weight $w$, we present criteria of the diameter two property and of the Radon-Nikod\\'ym property in Orlicz-Lorentz function and sequence spaces $\\Lambda_{\\varphi,w}$ and $\\lambda_{\\varphi,w}$. We show that in the spaces $\\Lambda_{\\varphi,w}$ or $\\lambda_{\\varphi,w}$ equipped with the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these spaces is two if and only if $\\varphi$ does not satisfy the appropriate $\\Delta_2$ condition, while they have the Radon-Nikod\\'ym property if and only if $\\varphi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00909","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"}