Preservers of local spectrum of matrix Jordan triple products

Let Mn be the space of n×n complex matrices, and for a nonzero vector e∈Cn and T∈Mn, let σT(e) denote the local spectrum of T at e. Maps ϕ on Mn which preserve the local spectrum of Jordan triple product of matrices at e in a sense thatσϕ(T)ϕ(S)ϕ(T)(e)=σTST(e),(T,S∈Mn) are characterized, with no surjectivity assumption on them.