{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BS2AHNL6LI4QVA2EYVGS5NG2AG","short_pith_number":"pith:BS2AHNL6","schema_version":"1.0","canonical_sha256":"0cb403b57e5a390a8344c54d2eb4da0181091298ba027bf4f3e1100f69a965ff","source":{"kind":"arxiv","id":"1411.0134","version":1},"attestation_state":"computed","paper":{"title":"Gruss inequality for some types of positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA"],"primary_cat":"math.FA","authors_text":"Jagjit Singh Matharu, Mohammad Sal Moslehian","submitted_at":"2014-11-01T16:29:30Z","abstract_excerpt":"Assuming a unitarily invariant norm $|||\\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\\cdot|||$ on matrix algebras $\\mathcal{M}_n$ for all finite values of $n$ via $|||A|||=|||A\\oplus 0|||$. We show that if $\\mathscr{A}$ is a $C^*$-algebra of finite dimension $k$ and $\\Phi: \\mathscr{A} \\to \\mathcal{M}_n$ is a unital completely positive map, then \\begin{equation*} |||\\Phi(AB)-\\Phi(A)\\Phi(B)||| \\leq \\frac{1}{4} |||I_{n}|||\\,|||I_{kn}||| d_A d_B \\end{equation*} for any $A,B \\in \\mathscr{A}$, w"},"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":"1411.0134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-01T16:29:30Z","cross_cats_sorted":["math.CA","math.OA"],"title_canon_sha256":"d6531eb71b00ce6390ffabbd104e547825af2c579c3c390e7b02e620f303901b","abstract_canon_sha256":"ca7d6b528d05b9ed00d5274e9d09b3a743ef18a0ae3b95f78fc2d0a100e67163"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:38.536566Z","signature_b64":"jdqe113VSxYkaUDc/0ZseuJx4VSGKhM9yJn+gI2oB74QJdxuY3O2pAB+ndwEjz0flZTy965gkcPG/MZl8OnSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cb403b57e5a390a8344c54d2eb4da0181091298ba027bf4f3e1100f69a965ff","last_reissued_at":"2026-05-18T01:27:38.535939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:38.535939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gruss inequality for some types of positive linear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.OA"],"primary_cat":"math.FA","authors_text":"Jagjit Singh Matharu, Mohammad Sal Moslehian","submitted_at":"2014-11-01T16:29:30Z","abstract_excerpt":"Assuming a unitarily invariant norm $|||\\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\\cdot|||$ on matrix algebras $\\mathcal{M}_n$ for all finite values of $n$ via $|||A|||=|||A\\oplus 0|||$. We show that if $\\mathscr{A}$ is a $C^*$-algebra of finite dimension $k$ and $\\Phi: \\mathscr{A} \\to \\mathcal{M}_n$ is a unital completely positive map, then \\begin{equation*} |||\\Phi(AB)-\\Phi(A)\\Phi(B)||| \\leq \\frac{1}{4} |||I_{n}|||\\,|||I_{kn}||| d_A d_B \\end{equation*} for any $A,B \\in \\mathscr{A}$, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0134","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":"1411.0134","created_at":"2026-05-18T01:27:38.536055+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0134v1","created_at":"2026-05-18T01:27:38.536055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0134","created_at":"2026-05-18T01:27:38.536055+00:00"},{"alias_kind":"pith_short_12","alias_value":"BS2AHNL6LI4Q","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BS2AHNL6LI4QVA2E","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BS2AHNL6","created_at":"2026-05-18T12:28:22.404517+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/BS2AHNL6LI4QVA2EYVGS5NG2AG","json":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG.json","graph_json":"https://pith.science/api/pith-number/BS2AHNL6LI4QVA2EYVGS5NG2AG/graph.json","events_json":"https://pith.science/api/pith-number/BS2AHNL6LI4QVA2EYVGS5NG2AG/events.json","paper":"https://pith.science/paper/BS2AHNL6"},"agent_actions":{"view_html":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG","download_json":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG.json","view_paper":"https://pith.science/paper/BS2AHNL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0134&json=true","fetch_graph":"https://pith.science/api/pith-number/BS2AHNL6LI4QVA2EYVGS5NG2AG/graph.json","fetch_events":"https://pith.science/api/pith-number/BS2AHNL6LI4QVA2EYVGS5NG2AG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG/action/storage_attestation","attest_author":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG/action/author_attestation","sign_citation":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG/action/citation_signature","submit_replication":"https://pith.science/pith/BS2AHNL6LI4QVA2EYVGS5NG2AG/action/replication_record"}},"created_at":"2026-05-18T01:27:38.536055+00:00","updated_at":"2026-05-18T01:27:38.536055+00:00"}