{"paper":{"title":"On the dual of Ces\\`aro function space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anna Kami\\'nska, Damian Kubiak","submitted_at":"2011-09-25T21:33:51Z","abstract_excerpt":"The goal of this paper is to present an isometric representation of the dual space to Ces\\`aro function space $C_{p,w}$, $1<p<\\infty$, induced by arbitrary positive weight function $w$ on interval $(0,l)$ where $0<l\\leqslant\\infty$. For this purpose given a strictly decreasing nonnegative function $\\Psi$ on $(0,l)$, the notion of essential $\\Psi$-concave majorant $\\hat f$ of a measurable function $f$ is introduced and investigated. As applications it is shown that every slice of the unit ball of the Ces\\`aro function space has diameter 2. Consequently Ces\\`aro function spaces do not have the R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5400","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"}