{"paper":{"title":"Interpolation of Ces{\\`a}ro sequence and function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lech Maligranda, Sergey V. Astashkin","submitted_at":"2012-11-26T13:35:00Z","abstract_excerpt":"The interpolation property of Ces{\\`a}ro sequence and function spaces is investigated. It is shown that $Ces_p(I)$ is an interpolation space between $Ces_{p_0}(I)$ and $Ces_{p_1}(I)$ for $1 < p_0 < p_1 \\leq \\infty$ and $1/p = (1 - \\theta)/p_0 + \\theta /p_1$ with $0 < \\theta < 1$, where $I = [0, \\infty)$ or $[0, 1]$. The same result is true for Ces{\\`a}ro sequence spaces. On the other hand, $Ces_p[0, 1]$ is not an interpolation space between $Ces_1[0, 1]$ and $Ces_{\\infty}[0, 1]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5947","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"}