{"paper":{"title":"Optimality of the rearrangement inequality with applications to Lorentz-type sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ben Wallis, Denny Leung, Fernando Albiac, Jose L. Ansorena","submitted_at":"2017-05-10T19:55:22Z","abstract_excerpt":"We characterize the sequences $(w_i)_{i=1}^\\infty$ of non-negative numbers for which \\[ \\sum_{i=1}^\\infty a_i w_i \\quad \\text{ is of the same order as } \\quad \\sup_n \\sum_{i=1}^n a_i w_{1+n-i} \\] when $(a_i)_{i=1}^\\infty$ runs over all non-increasing sequences of non-negative numbers. As a by-product of our work we settle a problem raised in [F. Albiac, Jose L. Ansorena and B. Wallis; arXiv:1703.07772[math.FA]] and prove that Garling sequences spaces have no symmetric basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03936","kind":"arxiv","version":2},"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"}