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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.02977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-08T08:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"8760d379c7cadd2166089878589d135124b9820a9bc0d3e9f61a8951a12fb061","abstract_canon_sha256":"e9cbca750e55fc27489d505e0c9228c098ce52250ffe52e154b2c65eaf9a2397"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:56:36.188402Z","signature_b64":"nFmlZ5lIYdUhwBXVh3wneeM/vIS2T8RI55vWquC5xK9hQMnqYHpS7nM9hx4E9wZhrk1mPbkJoBVgkVr8Rki0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce8b103e03110755e2d773f33c7cc5be274bc99ac423ef7f25f54dd94033b96e","last_reissued_at":"2026-07-04T23:56:36.187953Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:56:36.187953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.02977","created_at":"2026-07-04T23:56:36.188008+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02977v2","created_at":"2026-07-04T23:56:36.188008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02977","created_at":"2026-07-04T23:56:36.188008+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2FRAPQDCEDV","created_at":"2026-07-04T23:56:36.188008+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2FRAPQDCEDVLYWX","created_at":"2026-07-04T23:56:36.188008+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2FRAPQD","created_at":"2026-07-04T23:56:36.188008+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY","json":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY.json","graph_json":"https://pith.science/api/pith-number/Z2FRAPQDCEDVLYWXOPZTY7GFXY/graph.json","events_json":"https://pith.science/api/pith-number/Z2FRAPQDCEDVLYWXOPZTY7GFXY/events.json","paper":"https://pith.science/paper/Z2FRAPQD"},"agent_actions":{"view_html":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY","download_json":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY.json","view_paper":"https://pith.science/paper/Z2FRAPQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02977&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2FRAPQDCEDVLYWXOPZTY7GFXY/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2FRAPQDCEDVLYWXOPZTY7GFXY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY/action/storage_attestation","attest_author":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY/action/author_attestation","sign_citation":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY/action/citation_signature","submit_replication":"https://pith.science/pith/Z2FRAPQDCEDVLYWXOPZTY7GFXY/action/replication_record"}},"created_at":"2026-07-04T23:56:36.188008+00:00","updated_at":"2026-07-04T23:56:36.188008+00:00"}