{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4J2CMUIHPEFURBXWO3ANJKXM33","short_pith_number":"pith:4J2CMUIH","schema_version":"1.0","canonical_sha256":"e274265107790b4886f676c0d4aaecdededa4214a9af46519e243e887fde4448","source":{"kind":"arxiv","id":"1405.5715","version":1},"attestation_state":"computed","paper":{"title":"Uniqueness of the maximal ideal of operators on the $\\ell_p$-sum of $\\ell_\\infty^n\\ (n\\in\\mathbb{N})$ for $1<p<\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2014-05-22T11:27:39Z","abstract_excerpt":"A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_p}$ and $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_1^n\\bigr)_{\\ell_p}$ whenever $p\\in(1,\\infty)$."},"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":"1405.5715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-22T11:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"73060293f2541fa209fdee80b71824842f81b543879d0351ca4016b79de769bc","abstract_canon_sha256":"559355b94ef1f8725769f2bd65ec770ab39c383e9dc235195337136519a63e3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:44.311692Z","signature_b64":"v0y2dFHhcnNxZ4LxK4KuhdezVupzWhy3n+O/fMUjCZZmejbXOHq4iEPrc6H0eXIMUXQ7QT2BvmkqiEFwg7qNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e274265107790b4886f676c0d4aaecdededa4214a9af46519e243e887fde4448","last_reissued_at":"2026-05-18T01:17:44.311090Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:44.311090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of the maximal ideal of operators on the $\\ell_p$-sum of $\\ell_\\infty^n\\ (n\\in\\mathbb{N})$ for $1<p<\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Niels Jakob Laustsen, Tomasz Kania","submitted_at":"2014-05-22T11:27:39Z","abstract_excerpt":"A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_\\infty^n\\bigr)_{\\ell_p}$ and $X=\\bigl(\\bigoplus_{n\\in\\mathbb{N}}\\ell_1^n\\bigr)_{\\ell_p}$ whenever $p\\in(1,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5715","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":"1405.5715","created_at":"2026-05-18T01:17:44.311175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.5715v1","created_at":"2026-05-18T01:17:44.311175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5715","created_at":"2026-05-18T01:17:44.311175+00:00"},{"alias_kind":"pith_short_12","alias_value":"4J2CMUIHPEFU","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4J2CMUIHPEFURBXW","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4J2CMUIH","created_at":"2026-05-18T12:28:14.216126+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/4J2CMUIHPEFURBXWO3ANJKXM33","json":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33.json","graph_json":"https://pith.science/api/pith-number/4J2CMUIHPEFURBXWO3ANJKXM33/graph.json","events_json":"https://pith.science/api/pith-number/4J2CMUIHPEFURBXWO3ANJKXM33/events.json","paper":"https://pith.science/paper/4J2CMUIH"},"agent_actions":{"view_html":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33","download_json":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33.json","view_paper":"https://pith.science/paper/4J2CMUIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.5715&json=true","fetch_graph":"https://pith.science/api/pith-number/4J2CMUIHPEFURBXWO3ANJKXM33/graph.json","fetch_events":"https://pith.science/api/pith-number/4J2CMUIHPEFURBXWO3ANJKXM33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33/action/storage_attestation","attest_author":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33/action/author_attestation","sign_citation":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33/action/citation_signature","submit_replication":"https://pith.science/pith/4J2CMUIHPEFURBXWO3ANJKXM33/action/replication_record"}},"created_at":"2026-05-18T01:17:44.311175+00:00","updated_at":"2026-05-18T01:17:44.311175+00:00"}