Dual space valued mappings on C*-algebras which are ternary derivable at zero

Abstract

Extending derivability of a mapping from one point of a C*-algebra to the entire space is one of the interesting problems in derivation theory. In this paper, by considering a C*-algebra A as a Jordan triple with triple product {a,b,c}=(ab*c+cb*a)/2, and its dual space as a ternary A-module, we prove that a continuous conjugate linear mapping T from A into its dual space is a ternary derivation whenever it is ternary derivable at zero and the element T(1) is skew-symmetric.