Jordan *-triple derivations on the exceptional Cartan factors

Abstract Let U be any of the two exceptional Cartan factors V and VI and let δ : U → U be a Jordan *-triple derivation of U, that is, a map (neither linearity nor continuity of δ is assumed) that satisfies the functional equation δ { a b ⁎ a } = { δ ( a ) b ⁎ a } + { a δ ( b ) ⁎ a } + { a b ⁎ δ ( a ) } , ( a , b ∈ U ) , where ( a , b ) ↦ { a b ⁎ a } stands for the Jordan triple product in U. We give an explicit representation of δ as certain multipliers on U and prove that δ automatically is a continuous real linear map on U. This gives a new description of the real Banach Lie algebra of Jordan triple derivations of U.