{"paper":{"title":"Abstract Ces\\`aro Spaces. I. Duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Karol Le\\'snik, Lech Maligranda","submitted_at":"2014-01-24T18:09:27Z","abstract_excerpt":"We study abstract Ces\\`aro spaces $CX$, which may be regarded as generalizations of Ces\\`aro sequence spaces $ces_p$ and Ces\\`aro function spaces $Ces_p(I)$ on $I = [0,1]$ or $I = [0,\\infty)$, and also as the description of optimal domain from which Ces\\`aro operator acts to $X$. We find the dual of such spaces in a very general situation. What is however even more important, we do it in the simplest possible way. Our proofs are more elementary than the known ones for $ces_p$ and $Ces_p(I)$. This is the point how our paper should be seen, i.e. not as generalization of known results, but rather"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6415","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"}