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 >