LIE TRIPLE DERIVATIONS ON FACTOR VON NEUMANN ALGEBRAS
LIE TRIPLE DERIVATIONS ON FACTOR VON NEUMANN ALGEBRAS
Let <TEX>$\mathcal{A}$</TEX> be a factor von Neumann algebra with dimension greater than 1. We prove that if a linear map <TEX>${\delta}:\mathcal{A}{\rightarrow}\mathcal{A}$</TEX> satisfies <TEX>$${\delta}([[a,b],c])=[[{\delta}(a),b],c]+[[a,{\delta}(b),c]+[[a,b],{\delta}(c)]$$</TEX> for any <TEX>$a,b,c{\in}\mathcal{A}$</TEX> with ab = 0 (resp. ab = P, where P is a fixed nontrivial projection of <TEX>$\mathcal{A}$</TEX>), then there exist an operator <TEX>$T{\in}\mathcal{A}$</TEX> and …