Maps preserving n-tuple A*B − B*A derivations on factor von Neumann algebras

Abstract

Let A be a factor von Neumann algebra and ? preserve n-tuple new product derivations on A, that is, for every A1,A2,... ,An ? A, ?(A1 ? A2 ?...? An) = ?(A1) ? A2 ?...? An + A1 ? ?(A2) ?... ? An + ... + A1 ? A2 ? ... ? ?(An) where Ai ?Aj = A*iAj ?A*jAi for i,j ? N, then ? is additive *-derivation, on the condition that ?(?I/2) is self-adjoint operator for ? ? {1,i}.