{"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. Let both $\\varphi: B({\\mathcal{H}},{\\mathcal{K}})\\rightarrow B({\\mathcal{H}},{\\mathcal{K}})$ and $\\psi: B({\\mathcal{K}},{\\mathcal{H}})\\ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4455","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}