Abstract
As a generalization of global mappings,we study a class of non-global map-pings in this note.Let A ⊆ B(H)be a von Neumann algebra without abelian direct summands.We prove that if a map δ:A →A satisfies δ([[A,B]*,C])=[[δ(A),B]*,C]+[[A,δ(B)]*,C]+[[A,B]*,δ(C)]for any A,B,C ∈ A with A*B*C=0,then δ is an additive*-derivation.As applications,our results are applied to factor von Neumann algebras,standard operator algebras,prime*-algebras and so on.
基金项目
Scientific and Technological Innovation Programs of Higher Education Programs in Shanxi(2021L015)
Fundamental Research Program of Shanxi Province(202103021223038)
NETL
NSTL
万方数据