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Let 1<p<infinity and suppose that x in B(H) is an operator such that the commutator [A, x] is contained in the Schatten class S_p. It is proved by the last two authors, that then also [f(A), x] is contained in S_p and there exists a constant C_p independent of x and f such that || [f(A), x] ||_p <= C_p || [A,x] ||_p.\n  The main result of this paper is to give a sharp estimate for C_p in terms of p. Namely, we show that C_p ~ p^"},"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":"1209.3948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-18T13:17:10Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3af880d98032800161a64a88c364c39865c10d20b0358de700ca66537dfde5ad","abstract_canon_sha256":"552fa8a642acb0840d9b28949d5546f56486bbb2b6f40c5f7241f9e7df197779"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.131032Z","signature_b64":"SOu8Kj6iSqSA6mxVnR0Tg2nsZDJDKNrLLSnvfV+RexNim7brOTV1aoxsgDctjSToaRkx0RTTWyRmnZZ8Z8xQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2ebe8d8419accffadc4a06eecbf7c07901e8811337e9c4871e5144c42711014","last_reissued_at":"2026-05-18T02:44:07.130566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.130566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The best constants for operator Lipschitz functions on Schatten classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Denis Potapov, Fedor Sukochev, Martijn Caspers, Stephen Montgomery-Smith","submitted_at":"2012-09-18T13:17:10Z","abstract_excerpt":"Suppose that f is a Lipschitz function on the real numbers with Lipschitz constant smaller or equal to 1. 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