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This implies an inequality due to Livshits and two apparently new ones on diagonals of matrices. ||A (*) B|| \\leq ||A||_r ||B||_c operator, row and column norm; - diag(A*A) \\leq A* (*) A \\leq diag(A*A), and for all vectors f, g: |<A(*)B f,g> |^2 \\leq < "},"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":"1712.05285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"8b655e5754b6a987dd8a54c6e9fc55b0b99b3e4d8d552fdbf4d0a713dfa40bc7","abstract_canon_sha256":"244375dfd30df9b5f572d918b7dcb5e0097ec318428c2ec6866be4f4a8b4b141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.217868Z","signature_b64":"gmZULeWwAu+sLKMJgXY+fhSSbXNPftioBv2WvgdVdmnmwhbOM16EVsPNOHTYpenEn0+8TTxz1qfAtDGGaUHJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","last_reissued_at":"2026-05-18T00:01:15.217443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.217443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the complete boundedness of the Schur block product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.OA","authors_text":"Erik Christensen","submitted_at":"2017-12-14T15:30:16Z","abstract_excerpt":"We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_{ij}), B:= (b_{ij}): A (*) B := (a_{ij}b_{ij}) = V* pi(A) F pi(B) V, such that V is an isometry, pi is a *-representation and F is a self-adjoint unitary. This implies an inequality due to Livshits and two apparently new ones on diagonals of matrices. ||A (*) B|| \\leq ||A||_r ||B||_c operator, row and column norm; - diag(A*A) \\leq A* (*) A \\leq diag(A*A), and for all vectors f, g: |<A(*)B f,g> |^2 \\leq < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05285","kind":"arxiv","version":3},"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":"1712.05285","created_at":"2026-05-18T00:01:15.217519+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.05285v3","created_at":"2026-05-18T00:01:15.217519+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05285","created_at":"2026-05-18T00:01:15.217519+00:00"},{"alias_kind":"pith_short_12","alias_value":"AB4LXUFM65FB","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AB4LXUFM65FBWX7S","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AB4LXUFM","created_at":"2026-05-18T12:31:05.417338+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/AB4LXUFM65FBWX7SMEYZRZI67N","json":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N.json","graph_json":"https://pith.science/api/pith-number/AB4LXUFM65FBWX7SMEYZRZI67N/graph.json","events_json":"https://pith.science/api/pith-number/AB4LXUFM65FBWX7SMEYZRZI67N/events.json","paper":"https://pith.science/paper/AB4LXUFM"},"agent_actions":{"view_html":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N","download_json":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N.json","view_paper":"https://pith.science/paper/AB4LXUFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.05285&json=true","fetch_graph":"https://pith.science/api/pith-number/AB4LXUFM65FBWX7SMEYZRZI67N/graph.json","fetch_events":"https://pith.science/api/pith-number/AB4LXUFM65FBWX7SMEYZRZI67N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/action/storage_attestation","attest_author":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/action/author_attestation","sign_citation":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/action/citation_signature","submit_replication":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/action/replication_record"}},"created_at":"2026-05-18T00:01:15.217519+00:00","updated_at":"2026-05-18T00:01:15.217519+00:00"}