Triple derivable maps on prime algebras with involution

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.