{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FBWXIHIINRRGV5YXGMCB3VWTLN","short_pith_number":"pith:FBWXIHII","schema_version":"1.0","canonical_sha256":"286d741d086c626af71733041dd6d35b7c937ae19489f784c7f898b130ee7abd","source":{"kind":"arxiv","id":"1504.01189","version":1},"attestation_state":"computed","paper":{"title":"Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Aleksei Aleksandrov, Fedor Nazarov, Vladimir Peller","submitted_at":"2015-04-06T02:30:26Z","abstract_excerpt":"We study perturbations of functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\\be,1}^1(\\R^2)$, then we have the following Lipschitz type estimate in the Schatten--von Neumann norm $\\bS_p$, $1\\le p\\le2$ norm: $\\|f(A_1,B_1)-f(A_2,B_2)\\|_{\\bS_p}\\le\\const(\\|A_1-A_2\\|_{\\bS_p}+\\|B_1-B_2\\|_{\\bS_p})$. However, the condition $f\\in B_{\\be,1}^1(\\R^2)$ does not imply the Lipschitz type estimate in $\\bS_p$ with $p>2$. The main tool is Schatten--von Neumann norm estimates for trip"},"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":"1504.01189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T02:30:26Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"020267037e5937cce4683acb1333966b652455d0da8bc9dff12cd195e6a2d10a","abstract_canon_sha256":"6e1aa9c07b4a56271e9e3ebd765fb6a045c75a2c28dc5e44944f46ce62149d5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:34.941872Z","signature_b64":"62xBQ2T5yvX5TN8ah2Ec/EolpflmzkzysiDZpo1I1AEL56eXIdckssFZc/GlopSXhKPN3Y0+XTbFzrQwpgzIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"286d741d086c626af71733041dd6d35b7c937ae19489f784c7f898b130ee7abd","last_reissued_at":"2026-05-18T02:19:34.941386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:34.941386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Aleksei Aleksandrov, Fedor Nazarov, Vladimir Peller","submitted_at":"2015-04-06T02:30:26Z","abstract_excerpt":"We study perturbations of functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\\be,1}^1(\\R^2)$, then we have the following Lipschitz type estimate in the Schatten--von Neumann norm $\\bS_p$, $1\\le p\\le2$ norm: $\\|f(A_1,B_1)-f(A_2,B_2)\\|_{\\bS_p}\\le\\const(\\|A_1-A_2\\|_{\\bS_p}+\\|B_1-B_2\\|_{\\bS_p})$. However, the condition $f\\in B_{\\be,1}^1(\\R^2)$ does not imply the Lipschitz type estimate in $\\bS_p$ with $p>2$. The main tool is Schatten--von Neumann norm estimates for trip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01189","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":"1504.01189","created_at":"2026-05-18T02:19:34.941456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01189v1","created_at":"2026-05-18T02:19:34.941456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01189","created_at":"2026-05-18T02:19:34.941456+00:00"},{"alias_kind":"pith_short_12","alias_value":"FBWXIHIINRRG","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FBWXIHIINRRGV5YX","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FBWXIHII","created_at":"2026-05-18T12:29:19.899920+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/FBWXIHIINRRGV5YXGMCB3VWTLN","json":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN.json","graph_json":"https://pith.science/api/pith-number/FBWXIHIINRRGV5YXGMCB3VWTLN/graph.json","events_json":"https://pith.science/api/pith-number/FBWXIHIINRRGV5YXGMCB3VWTLN/events.json","paper":"https://pith.science/paper/FBWXIHII"},"agent_actions":{"view_html":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN","download_json":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN.json","view_paper":"https://pith.science/paper/FBWXIHII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01189&json=true","fetch_graph":"https://pith.science/api/pith-number/FBWXIHIINRRGV5YXGMCB3VWTLN/graph.json","fetch_events":"https://pith.science/api/pith-number/FBWXIHIINRRGV5YXGMCB3VWTLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN/action/storage_attestation","attest_author":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN/action/author_attestation","sign_citation":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN/action/citation_signature","submit_replication":"https://pith.science/pith/FBWXIHIINRRGV5YXGMCB3VWTLN/action/replication_record"}},"created_at":"2026-05-18T02:19:34.941456+00:00","updated_at":"2026-05-18T02:19:34.941456+00:00"}