Let A be a prime -algebra and suppose that 8 preserves triple -Jordan derivation on A, that is, for every A; B 2 A, 8.A B C/ D 8.A/ B C C A 8.B/ C C A B 8.C/; where A B D AB C B A. Then 8 is additive. Moreover, if 8. I / is selfadjoint for 2 f1; ig, then 8 is a -derivation.
