On normal ternary weak amenability of factors

We show that the norm closure of the set of inner triple derivations from a factor von Neumann algebra into its predual, has codimension zero or one in the real vector space of all triple derivations. It is zero if and only if the factor is finite. We also prove that every Jordan derivation of a von Neumann algebra to itself is an inner Jordan derivation and give a new proof that every triple derivation of a von Neumann algebra to itself is an inner triple derivation.

(A revised version with a different title was published: Triple derivations on von Neumann algebras. Studia Math. 226 (2015), no. 1, 57-73)


Robert Pluta < robert-pluta@uiowa.edu >

Bernard Russo < brusso@uci.edu >