{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3NP5K2NSZ6PQEL3GZA6A43GO2Z","short_pith_number":"pith:3NP5K2NS","schema_version":"1.0","canonical_sha256":"db5fd569b2cf9f022f66c83c0e6cced6496a2e0921c69c1fc39d2c8582173b47","source":{"kind":"arxiv","id":"1709.01850","version":1},"attestation_state":"computed","paper":{"title":"Numerical radius inequalities involving commutators of $G_{1}$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Fuad Kittaneh, Mojtaba Bakherad","submitted_at":"2017-09-05T13:24:58Z","abstract_excerpt":"We prove numerical radius inequalities involving commutators of $G_{1}$ operators and certain analytic functions. Among other inequalities, it is shown that if $A$ and $X$ are bounded linear operators on a complex Hilbert space, then \\begin{equation*} w(f(A)X+X\\bar{f}(A))\\leq {\\frac{2}{d_{A}^{2}}}w(X-AXA^{\\ast }), \\end{equation*} where $A$ is a $G_{1}$ operator with $\\sigma (A)\\subset \\mathbb{D}$ and $f$ is analytic on the unit disk $\\mathbb{D}$ such that $\\textrm{{Re}}(f)>0$ and $f(0)=1$."},"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":"1709.01850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-09-05T13:24:58Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"15ba8ed60e1ecb53304bdae8e68bfbb126919dbf2d712fee0d08881844a0f8e7","abstract_canon_sha256":"cf48a5ea5780ad21c043724d3f8db2c52472649945944db32fde707bb33ca7d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:54.208400Z","signature_b64":"H563h/9k7A1+LKCkxbNHMmx1dZF31RCjYyBShjPjhkn4iC8GkBxUP4P8n5MTmwi3Sc89eY9L0lmKEJCP6uTGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db5fd569b2cf9f022f66c83c0e6cced6496a2e0921c69c1fc39d2c8582173b47","last_reissued_at":"2026-05-18T00:35:54.207952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:54.207952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical radius inequalities involving commutators of $G_{1}$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Fuad Kittaneh, Mojtaba Bakherad","submitted_at":"2017-09-05T13:24:58Z","abstract_excerpt":"We prove numerical radius inequalities involving commutators of $G_{1}$ operators and certain analytic functions. Among other inequalities, it is shown that if $A$ and $X$ are bounded linear operators on a complex Hilbert space, then \\begin{equation*} w(f(A)X+X\\bar{f}(A))\\leq {\\frac{2}{d_{A}^{2}}}w(X-AXA^{\\ast }), \\end{equation*} where $A$ is a $G_{1}$ operator with $\\sigma (A)\\subset \\mathbb{D}$ and $f$ is analytic on the unit disk $\\mathbb{D}$ such that $\\textrm{{Re}}(f)>0$ and $f(0)=1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01850","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":"1709.01850","created_at":"2026-05-18T00:35:54.208021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.01850v1","created_at":"2026-05-18T00:35:54.208021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01850","created_at":"2026-05-18T00:35:54.208021+00:00"},{"alias_kind":"pith_short_12","alias_value":"3NP5K2NSZ6PQ","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3NP5K2NSZ6PQEL3G","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3NP5K2NS","created_at":"2026-05-18T12:30:58.224056+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/3NP5K2NSZ6PQEL3GZA6A43GO2Z","json":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z.json","graph_json":"https://pith.science/api/pith-number/3NP5K2NSZ6PQEL3GZA6A43GO2Z/graph.json","events_json":"https://pith.science/api/pith-number/3NP5K2NSZ6PQEL3GZA6A43GO2Z/events.json","paper":"https://pith.science/paper/3NP5K2NS"},"agent_actions":{"view_html":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z","download_json":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z.json","view_paper":"https://pith.science/paper/3NP5K2NS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.01850&json=true","fetch_graph":"https://pith.science/api/pith-number/3NP5K2NSZ6PQEL3GZA6A43GO2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/3NP5K2NSZ6PQEL3GZA6A43GO2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z/action/storage_attestation","attest_author":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z/action/author_attestation","sign_citation":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z/action/citation_signature","submit_replication":"https://pith.science/pith/3NP5K2NSZ6PQEL3GZA6A43GO2Z/action/replication_record"}},"created_at":"2026-05-18T00:35:54.208021+00:00","updated_at":"2026-05-18T00:35:54.208021+00:00"}