{"paper":{"title":"Strong skew commutativity preserving maps on von Neumann algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"Jinchuan Hou, Xiaofei Qi","submitted_at":"2012-04-09T09:49:50Z","abstract_excerpt":"Let ${\\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$. Assume that $\\Phi:{\\mathcal M}\\rightarrow {\\mathcal M}$ is a surjective map. It is shown that $\\Phi$ is strong skew commutativity preserving (that is, satisfies $\\Phi(A)\\Phi(B)-\\Phi(B)\\Phi(A)^*=AB-BA^*$ for all $A,B\\in{\\mathcal M}$) if and only if there exists some self-adjoint element $Z$ in the center of ${\\mathcal M}$ with $Z^2=I$ such that $\\Phi(A)=ZA$ for all $A\\in{\\mathcal M}$. The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1841","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"}