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When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm \\eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a rando"},"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":"1302.4849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-20T09:39:45Z","cross_cats_sorted":[],"title_canon_sha256":"78a55d20f016e294aa21f1e61b8c6b8b02692349ebf2fbec45b8c09fc0846010","abstract_canon_sha256":"3eddbdc70e54089d437a98df03c90124ce805fb32199f004ab9e8d22d7c73fe4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:47.230086Z","signature_b64":"zhvSICWcm2T2zGQHwWEkhmTxk4bc18a9qEkuA6BWrv00xe8Dt1mhR3AxS8bogJoDIPEauC8UWyW9Drjj/MfiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be5690d7d908e722eee24e31d03c2739e4f56a8d9625126f9a71b94fe6a201b2","last_reissued_at":"2026-05-18T02:49:47.229602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:47.229602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norms of idempotent Schur multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rupert H. 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We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a rando"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4849","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":""},"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":"1302.4849","created_at":"2026-05-18T02:49:47.229668+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4849v2","created_at":"2026-05-18T02:49:47.229668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4849","created_at":"2026-05-18T02:49:47.229668+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZLJBV6ZBDTS","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZLJBV6ZBDTSF3XC","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZLJBV6Z","created_at":"2026-05-18T12:28:06.772260+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/XZLJBV6ZBDTSF3XCJYY5APBHHH","json":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH.json","graph_json":"https://pith.science/api/pith-number/XZLJBV6ZBDTSF3XCJYY5APBHHH/graph.json","events_json":"https://pith.science/api/pith-number/XZLJBV6ZBDTSF3XCJYY5APBHHH/events.json","paper":"https://pith.science/paper/XZLJBV6Z"},"agent_actions":{"view_html":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH","download_json":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH.json","view_paper":"https://pith.science/paper/XZLJBV6Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4849&json=true","fetch_graph":"https://pith.science/api/pith-number/XZLJBV6ZBDTSF3XCJYY5APBHHH/graph.json","fetch_events":"https://pith.science/api/pith-number/XZLJBV6ZBDTSF3XCJYY5APBHHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/action/storage_attestation","attest_author":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/action/author_attestation","sign_citation":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/action/citation_signature","submit_replication":"https://pith.science/pith/XZLJBV6ZBDTSF3XCJYY5APBHHH/action/replication_record"}},"created_at":"2026-05-18T02:49:47.229668+00:00","updated_at":"2026-05-18T02:49:47.229668+00:00"}