Jordan triple maps. (Q1414719)

Let \(r\) be a nonzero rational number. A map \(\phi : A \to B\) between Banach algebras \(A\) and \(B\) is said to be a \(r\)-Jordan triple map if \(\phi(r(abc+cba)) = r(\phi(a)\phi(b)\phi(c)+\phi(c)\phi(b)\phi(a))\) for all \(a,b,c \in A\). Suppose that \(A\) is a standard operator algebra. The author proves, among other things, that a bijective \(r\)-Jordan triple map is necessarily additive.