  A well known result of Haagerup from 1983 states that every C*-algebra A is
weakly amenable, that is, every (associative) derivation from A into its dual
is inner. A Banach algebra B is said to be ternary weakly amenable if every
continuous Jordan triple derivation from B into its dual is inner. We show that
commutative C*-algebras are ternary weakly amenable, but that B(H) and K(H) are
not, unless H is finite dimensional. More generally, we inaugurate the study of
weak amenability for Jordan Banach triples, focussing on commutative
JB*-triples and some Cartan factors.
