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If $A$ is a prime $C^*$-algebra and $\\sigma$ is surjective, we determine the structure of generalized $\\sigma$-derivations of $A$ that belong to the cb-norm closure of elementary operators $\\mathcal{E}\\ell(A)$ on $A$; all such maps are of the form $d(x)=bx+axc$ for suitable elements $a,b,c$ of the multiplier algebra $M(A)$. As a consequence, if"},"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":"1906.05548","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-13T08:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"06dc8a2202270c6744aabbe71f637a4a88b470af6fa5881f2ddc88c59fce6052","abstract_canon_sha256":"febbc1826958df16399b33b3008beb0548e21ded24b3b83f06a0da6055f008e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:21.607157Z","signature_b64":"uUdL6sIUamH4ZUvJ14+wpSZTPy6uSsnr+s4d1hZW0loSayvzjGRfM21qjceESG2nam8lGMMVsC2SCNwIPRM1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65dc98b8fecdabed38a350d3e39ecfcbadf4fe7f97e78d75bf1d46e264226f5","last_reissued_at":"2026-05-17T23:41:21.606580Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:21.606580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The cb-norm approximation of generalized skew derivations by elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ilja Gogi\\'c","submitted_at":"2019-06-13T08:40:19Z","abstract_excerpt":"Let $A$ be a ring and $\\sigma: A \\to A$ a ring endomorphism. A generalized skew (or $\\sigma$-)derivation of $A$ is an additive map $d: A \\to A$ for which there exists a map $\\delta:A \\to A$ such that $d(xy)=\\delta(x)y+\\sigma(x)d(y)$ for all $x,y \\in A$. If $A$ is a prime $C^*$-algebra and $\\sigma$ is surjective, we determine the structure of generalized $\\sigma$-derivations of $A$ that belong to the cb-norm closure of elementary operators $\\mathcal{E}\\ell(A)$ on $A$; all such maps are of the form $d(x)=bx+axc$ for suitable elements $a,b,c$ of the multiplier algebra $M(A)$. 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