{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1992:NGJQJTWU6BDFLUOKCUUHFXZHB7","short_pith_number":"pith:NGJQJTWU","schema_version":"1.0","canonical_sha256":"699304ced4f04655d1ca152872df270fe22057fa2c5b6dfd7c7e4918048ced4e","source":{"kind":"arxiv","id":"math/9210206","version":1},"attestation_state":"computed","paper":{"title":"Interpolation of compact operators by the methods of Calder\\'on and Gustavsson-Peetre","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Cwikel, Nigel J. Kalton","submitted_at":"1992-10-08T15:45:24Z","abstract_excerpt":"Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\\to Y$ is a linear operator such that $T:X_0\\to Y_0$ is compact. We consider the question whether the operator $T:[X_0,X_1]_{\\theta}\\to [Y_0,Y_1]_{\\theta}$ is compact and show a positive answer under a variety of conditions. For example it suffices that $X_0$ be a UMD-space or that $X_0$ is reflexive and there is a Banach space so that $X_0=[W,X_1]_{\\alpha}$ for some $0<\\alpha<1.$"},"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":"math/9210206","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1992-10-08T15:45:24Z","cross_cats_sorted":[],"title_canon_sha256":"c603f83dd3cdaa8cc1b6da9ce7eafaa5196492a6ce907e026fb61f7ac0eecb74","abstract_canon_sha256":"7df809aff7f1c15b0182db5f2775df055ba3f16aa824a281b0a2f891452c7499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:52.586022Z","signature_b64":"PNmOiuOxFYJzLmxh1RLINKAIR05nHKljJ65iBlo799c4bJ29b0xh+zLGMh2Ai1C6Bxv+MEXAMX2d/2bryOUdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"699304ced4f04655d1ca152872df270fe22057fa2c5b6dfd7c7e4918048ced4e","last_reissued_at":"2026-05-18T01:05:52.585559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:52.585559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolation of compact operators by the methods of Calder\\'on and Gustavsson-Peetre","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Michael Cwikel, Nigel J. Kalton","submitted_at":"1992-10-08T15:45:24Z","abstract_excerpt":"Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\\to Y$ is a linear operator such that $T:X_0\\to Y_0$ is compact. We consider the question whether the operator $T:[X_0,X_1]_{\\theta}\\to [Y_0,Y_1]_{\\theta}$ is compact and show a positive answer under a variety of conditions. For example it suffices that $X_0$ be a UMD-space or that $X_0$ is reflexive and there is a Banach space so that $X_0=[W,X_1]_{\\alpha}$ for some $0<\\alpha<1.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9210206","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/9210206","created_at":"2026-05-18T01:05:52.585625+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9210206v1","created_at":"2026-05-18T01:05:52.585625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9210206","created_at":"2026-05-18T01:05:52.585625+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGJQJTWU6BDF","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGJQJTWU6BDFLUOK","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGJQJTWU","created_at":"2026-05-18T12:25:47.102015+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/NGJQJTWU6BDFLUOKCUUHFXZHB7","json":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7.json","graph_json":"https://pith.science/api/pith-number/NGJQJTWU6BDFLUOKCUUHFXZHB7/graph.json","events_json":"https://pith.science/api/pith-number/NGJQJTWU6BDFLUOKCUUHFXZHB7/events.json","paper":"https://pith.science/paper/NGJQJTWU"},"agent_actions":{"view_html":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7","download_json":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7.json","view_paper":"https://pith.science/paper/NGJQJTWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9210206&json=true","fetch_graph":"https://pith.science/api/pith-number/NGJQJTWU6BDFLUOKCUUHFXZHB7/graph.json","fetch_events":"https://pith.science/api/pith-number/NGJQJTWU6BDFLUOKCUUHFXZHB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7/action/storage_attestation","attest_author":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7/action/author_attestation","sign_citation":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7/action/citation_signature","submit_replication":"https://pith.science/pith/NGJQJTWU6BDFLUOKCUUHFXZHB7/action/replication_record"}},"created_at":"2026-05-18T01:05:52.585625+00:00","updated_at":"2026-05-18T01:05:52.585625+00:00"}