Determining Ternary derivation on von Neumann algebra and their applications

We give a characterization on ternary derivations of von Neumann algebra. In fact, we prove that every ternary derivation is a spatial ternary derivation. Then we present various applications of this result to determine other types of mappings: (right or left) centralizers and derivations through zero products, local (right or left) centralizers, left/right ideal preserving maps and, local (generalized) derivations of von Neumann algebra. Some of our results are generalizations of some previously known results.

کلیدواژه ها:

Derivaton ، Ternary derivation ، von Neumann algebra ، zero product