Local triple derivations from C$^*$-algebras into their iterated duals

Abstract

We show that every local triple derivation from a C$^*$-algebra into any of its iterated duals is a triple derivation. This result partially solves a problem posed by M. Burgos \emph{et al.} in [Bull. London Math. Soc. 46 (4), 709-724 (2014)].