Abstract:

be a factor von Neumann algebra and δ be a mapping from M into itself (without assumption of additivity or continuity), we can show that if δ satisfies mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A) for all A,B∈M, then δ is an additive derivation  using the method of decomposing matrix.

Key words: factor von Neumann algebras, (m,n) derivations, (m,n) Jordan derivations, derivations, inner derivations