{"paper":{"title":"Two remarks on the interpolation space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Daher","submitted_at":"2019-08-08T08:55:34Z","abstract_excerpt":"Dans ce travail, on montre que $(M(\\mathbb{T}),c_0(\\mathbb{Z}))_\\theta = (L^1,c_0(\\mathbb{Z}))_\\theta$, $0<\\theta <1$. Dans la suite on montre pour le couple d'interpolation $(C_0,C_1)$ trouv\\'e par Garling-Smith qu'il existe un isomorphisme $U_\\theta: (C_0,C_0+C_1)_{\\theta ,p}\\rightarrow (C_1,C_0+C_1)_{\\theta, p}$ (resp. $U_\\theta : (C_0,C_0+C_1)_\\theta \\rightarrow (C_1,C_0+C_1)_\\theta)$ tel que sa restriction \\`a $C_{\\theta, p}$ (resp. \\`a $C_\\theta)$ est un isomorphisme : $C_{\\theta, p} \\rightarrow C_{1-\\theta, p}$ (resp. $C_\\theta \\rightarrow C_{1-\\theta })$.\n  --\n  In this work we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02977","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02977/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}