Abstract
Let A be a unital prime *-algebra with characteristic not 2 and with a projection . Suppose that
is a map satisfying
for all
, where
denotes the symmetric Martindale algebra of quotients of A. It is shown that d is an additive triple derivation. Moreover, there exist
with
and an additive *-derivation
such that
for all
. The analogous results for prime locally matrix *-algebras, prime *-algebras with nonzero socle, factor von Neumann algebras and standard operator *-algebras on Hilbert spaces are also described.
Acknowledgments
The authors would like to thank the referee for the very thorough reading of the paper and valuable comments.