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We say that an element $G\\in B({\\mathcal{H}},{\\mathcal{H}})$ is an all-derivable point in $B({\\mathcal{H}},{\\mathcal{H}})$ if every derivable linear mapping $\\varphi$ at $G$ (i.e. $\\varphi(ST)=\\varphi(S)T+S\\varphi(T)$ for any $S,T\\in B(H)$ with $ST=G$) is a derivation. Let both $\\varphi: B({\\mathcal{H}},{\\mathcal{K}})\\rightarrow B({\\mathcal{H}},{\\mathcal{K}})$ and $\\psi: B({\\mathcal{K}},{\\mathcal{H}})\\ri"},"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":"1405.4455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-05-18T03:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"4ca87351d5d2f36ebd366f7db8a353ea98f03a83050c2780a87b6a66f1cc682f","abstract_canon_sha256":"c6212efff6267b5c2d473a78b8ad29a53816a4d5c215f62fcfefc09c75c4e847"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:40.811982Z","signature_b64":"WzgnDO1x9FoueQChHEP+jKDo9czt+1PYjpzKzIC3fgwvXQuFW8T/AJle1CREATMbesW8McPNX+XtaCvzoNsgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abb7cb2b46ee79fedb222b77920cd137ba8909d847a0894335b44afc8f10ec1a","last_reissued_at":"2026-05-18T02:51:40.811503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:40.811503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of all-derivable points in $B(H)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Changping Xiong, Jun Zhu, Pan Li","submitted_at":"2014-05-18T03:23:21Z","abstract_excerpt":"Let ${\\mathcal{K}}$ and ${\\mathcal{H}}$ be two Hilbert space, and let $B({\\mathcal{K}},{\\mathcal{H}})$ be the algebra of all bounded linear operators from ${\\mathcal{K}}$ into ${\\mathcal{H}}$. We say that an element $G\\in B({\\mathcal{H}},{\\mathcal{H}})$ is an all-derivable point in $B({\\mathcal{H}},{\\mathcal{H}})$ if every derivable linear mapping $\\varphi$ at $G$ (i.e. $\\varphi(ST)=\\varphi(S)T+S\\varphi(T)$ for any $S,T\\in B(H)$ with $ST=G$) is a derivation. 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