因子von Neumann代数上ξ-斜Jordan可导映射的一个刻画

A characterization of ξ-skew Jordan derivable mappings on factor von Neumann algebras

设R是维数大于1的因子von Neumann代数。对于给定的复数ξ且ξ≠0,如果映射δ:R→R满足对所有A,B∈R,有δ((A·B)ξ)=(δ(A)·B)ξ+(A·δ(B))ξ,那么δ是可加的*-导子且满足δ(ξA)=ξδ(A)。特别地,若von Neumann代数R是无限的Ⅰ型因子,给出了δ的具体刻画。

Let R be a factor von Neumann algebra with dim R>1.For given complex numberξandξ≠0,if a mapδ:R→R satisfiesδ((A·B)ξ)=(δ(A)·B)ξ+(A·δ(B))ξfor all A,B∈R,δis an additive*-derivation andδ(ξA)=ξδ(A).In particular,if the von Neumann algebra R is infinite typeⅠfactors,a concrete characterization of δ is given.