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A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self-adjoint operators for any $p\\ge1$"},"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":"1902.06346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-17T23:11:11Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"371f11ff61259445ab937034cb23c45a2505bf81bd9ab03b985e18337f59cfea","abstract_canon_sha256":"570d8dd095c5271118dc48e0e6b81aef77291c500a9ca88ace56c36d3e7f98b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:45.811462Z","signature_b64":"faco+pNSnGr0sac0U3l0Vid+kBSgvSE/O68noBLcpVnENTkA+kBou8eJ5lb+/+y1wM542kNkFuyS6mCDE7DCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"874cbf968fdd7630348e756c609b0d1f1578833f7aa6d34d23f297758d9de836","last_reissued_at":"2026-05-17T23:53:45.810686Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:45.810686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functions of noncommuting operators under perturbation of class $\\boldsymbol{S}_p$","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, Vladimir Peller","submitted_at":"2019-02-17T23:11:11Z","abstract_excerpt":"In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\\infty,1}^1({\\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ belong to the Schatten--von Neumann class $\\boldsymbol{S}_p$ but $f(A_2,B_2)-f(A_1,B_1)\\not\\in\\boldsymbol{S}_p$. 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