{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FBWXIHIINRRGV5YXGMCB3VWTLN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6e1aa9c07b4a56271e9e3ebd765fb6a045c75a2c28dc5e44944f46ce62149d5a","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T02:30:26Z","title_canon_sha256":"020267037e5937cce4683acb1333966b652455d0da8bc9dff12cd195e6a2d10a"},"schema_version":"1.0","source":{"id":"1504.01189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01189","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01189v1","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01189","created_at":"2026-05-18T02:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"FBWXIHIINRRG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FBWXIHIINRRGV5YX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FBWXIHII","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:b68fb7c774cd952bed61633c80b5ea023e59f0831ff1f265f272f3324ff00b1a","target":"graph","created_at":"2026-05-18T02:19:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Aleksei Aleksandrov, Fedor Nazarov, Vladimir Peller","cross_cats":["math.CA","math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T02:30:26Z","title":"Triple operator integrals in Schatten--von Neumann norms and functions of perturbed noncommuting operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01189","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:053c2d0ba686df8ec09bd348bfa2b47a169924d38216b0b30026dc5ae10ae57f","target":"record","created_at":"2026-05-18T02:19:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6e1aa9c07b4a56271e9e3ebd765fb6a045c75a2c28dc5e44944f46ce62149d5a","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-06T02:30:26Z","title_canon_sha256":"020267037e5937cce4683acb1333966b652455d0da8bc9dff12cd195e6a2d10a"},"schema_version":"1.0","source":{"id":"1504.01189","kind":"arxiv","version":1}},"canonical_sha256":"286d741d086c626af71733041dd6d35b7c937ae19489f784c7f898b130ee7abd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"286d741d086c626af71733041dd6d35b7c937ae19489f784c7f898b130ee7abd","first_computed_at":"2026-05-18T02:19:34.941386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:34.941386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62xBQ2T5yvX5TN8ah2Ec/EolpflmzkzysiDZpo1I1AEL56eXIdckssFZc/GlopSXhKPN3Y0+XTbFzrQwpgzIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:34.941872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:053c2d0ba686df8ec09bd348bfa2b47a169924d38216b0b30026dc5ae10ae57f","sha256:b68fb7c774cd952bed61633c80b5ea023e59f0831ff1f265f272f3324ff00b1a"],"state_sha256":"bced0b34558d35db50bc236cf8b16043ffc7904387b341a1ce25fa630b1a088d"}